This is some old stuff I've posted other places, so sorry if repeats some things.
I would note that, at the time, the title of Ard Ri didn't exist yet, so having that term used is inappropriate for the period.
Brian Boru created it with the abbot of Ard Macha (Armagh) to replace an older title, calling the new title 'Ard Rí na hÉireann' (Ard Ri, or Ard Ruire, intentionally sounding somewhat akin to the Irish rendering of the Latin title Imperator, as the Latin appellation for the title of 'Ard Ri' was 'Scotorum Imperator'; meaning Emperor of the Gaels/Irish, in Latin).
In the 800s, the archaic, looser title, 'Rí Érenn Uile', 'King of All Ireland', was used. In 867, the most recent one had been Máel Sechnaill mac Máele Ruanaid, who had only just died in 862; he had been effectively king of most of the Gaelic Irish by forcing the other kings to pay him tribute. His 'successor' on lists of high kings, Aed Finliath (Aed mac Neill; 'Finliath', or 'Fair Warrior' was used to distinguish him from his grandfather, also named Aed), despite warring with great success against the viking invaders (in 866 he had just run the Norse out of Ulster, using his kingdom, Ailech, as a base of operations to operate over most of the kingdoms in what is now considered 'Ulster') never actually was called 'Rí Érenn Uile', but instead 'Rí Teamhair'/Rex Temorie (King of Tara). He is called, in a much later poem, 'airdri Gaidhel' (High/Over-King of the Irish), but wasn't seen as such in his lifetime.
It may make sense to simply have no major towns at all in Ireland, except maybe for those founded by the Norse (but even then, many of those were very small; 'Dyflin', Dublin, had only been founded in 841, on the opposite side of the river from the older Gaelic village of Ath Cliath; Dyflin was better fortified though, having been planned as a small fortress and market, where as Baile Ath Cliath was more or less a fishing village, which passed out of memory after the Irish seized Dublin and called it Baile Ath Cliath instead of the old village, as well as 'Dubhlinn'). It may make more sense just to have 'castles', with shops and such in them, considering the major pre-town settlements of Ireland were just the major fortresses of various nobles, or the monastic settlements, themselves often pretty well defended. Though, some of them were pretty impressive; Casiel in Munster, now a much more elaborate castle, was built on a cliffside in the country with two ring walls and a central stone tower and manor, with a market/residential area between the two walls.
Also, there was no actual kingdom of 'Ulster' or 'Meath' at the time, at least, not what people now consider Ulster or Meath.
Modern counties Tyrone and Donegal made up the kingdom of Ailech, ruled by a northern Ui Neill clan (at the time, under Áed Findliath mac Néill), from the Grianán Ailich (a fortress in county Donegal, though Ailech's main markets and trade ports were in Tyrone, and on the Inishowen peninsula, specifically).
The east coast of Ulster was 'Ulidia' or 'Ulaid', a rump kingdom that had once ruled the area we associate with Ulster, until Niall of the Nine Hostages and his descendants carved it into petty kingdoms centuries prior. It was ruled by the aging Cathalan mac Indrechtaig and his younger third cousin Lethlobar mac Loingsig, who were given mutual rulership of the kingdom on the death of Matudán mac Muiredaig. They were loosely allied with Áed, for the purposes of running off viking raids, but also regularly raided into Ailech for cattle and slaves, and vice versa, (though they didn't campaign or outright attack eachothers major armies; old Gaelic warfare and politics is complicated, minding these things also applied to the Gaelic parts of what would become Scotland).
Also in Ulster, there was Airgialla, which wasn't really a kingdom at all; it was 9 small tribal kingdoms in a military confederation led by a king elected from among the noblemen of each tribe (though they almost always came from the three most powerful tribes at the time). The tribes were the (in rough order of power);
Ui Moccu Uais - Almost all of the federation's over-kings was from them at one point
Ui Meic Cairthinn - Actually a branch of the Ui Moccu Uais who had gained so much power they formed their own small kingdom
Ui Thuirtri
Ui Fhiachrach Arda Sratha
Ui Chremthainn
Ui Meith
Ui Cruinn
The last two are strange in that they don't have Gaelic tribe name caveats; they are not named Mac, Ui, Sil, or Dal (tribe name). They were the;
Mugdorna
Ind Airthir
They all nine claimed to all be related in the late 750s, as a means to solidify their alliance with the Ui Neill, but the truth is they probably weren't at all related until they began intermarrying heavily toward the end of the 770s, and even then, they weren't that closely related until about two centuries later. We don't actually know who was the over-king at the time.
Lastly, in Ulster and also part of Connacht, there was the kingdom of Breifne, which covered what is now county Leitrim and county Cavan, and eastern county Sligo. At the time, it was ruled by Ceallach mac Cearnach, of the Ui Briúin tribe. One of their offshoots, the Ui Ruairc clan, administered much of Leitrim, as well as the portion of Sligo controlled by Breifne, but were subjects of Ceallach, who was ruling from Cavan. They were relatives and allies of the ruling family of Connacht (the king of Connacht in 867 being Mugron mac Máel Cothaid), but were independent.
Meath was divided into the lands held by Clann Cholmáin, which was the kingdom of Uisnech, which was much of what is now West Meath, and the kingdom of Brega, held by the Síl nÁedo Sláine tribe, specifically the Ui Chonaing clan, under their king Flann mac Conaing (the 'Rí Brega', King of Brega), which controlled Teamhair (Tara), and some area south of what is now Dublin. The elderly Diarmait mac Etersceili administered southern Brega (holding the lesser title of 'Rí Locha Gabor', 'King of the Lake of Goats') until his death in 868; he was part of the Ui Chernaig clan, another branch of the Síl nÁedo Sláine, and a subordinate of Flann mac Conaing.
However, 'Dyflin' and its immediate surroundings were controlled by Norse-Gaels in their own tiny independent sub-kingdom, from which they often raided Brega, at the outset of 867.
Dyflin I'll seperate since their situation was complicated, but they did inhabit 'Meath'. Their regional king, the Norse-Gael Auisle, was killed by his brother Amlaib in a dispute involving Amlaib's wife, a princess of either the kingdom of Brega (most likely she was daughter of the former king, Cinaed mac Conaing) or the kingdom of the Picts (a daughter of Cinaed mac Alpin), early in 867. Amlaib, and his other brother, the Danish-styled 'Imar' (he was possibly Ivar Ragnarsson; 'Ivar the Boneless', the Irish called him Imar), effectively ruled Dublin until 873; while Ivar was technically king, Amlaíb Conung (or Óláfr, possibly 'Olaf the White'), who took to dressing as the Irish did, and spoke their language, actually administered the territory (though both took part on raids in Meath at different times), after he killed Auisle. The Dubliners were allies to the kings of Osraige (part of Leinster now), and the kings of Ailech, and all helped eachother raid Brega, and sometimes deeper, into Uisnech. Should note, while the Gaelic Irish kings in question were Christians, Amlaib and Ivar were pagans. Also, I mention Dublin here, as it was the 'kingdom of Dublin' (though, truthfully, it was all just part of Ivar Ragnarsson's larger kingdom, which included parts of Britain and other parts of Ireland, like Wicklow and Wexford).
In what's now Leinster, also, there wasn't one over-kingdom; there were two primary kingdoms (though, all of Ireland had many minor kingdoms, which I'm not bothering to mention, since they were technically just small vassalized petty-kingdoms that swore loyalty to the mentioned major kingdoms, though, where I think there's an important minor king to mention, like Diarmait mac Etersceili, I'll try to mention).
There was Laigin (Leinster), and Osraige. Osraige was the smaller one, but fairly powerful. Also notable is that, when vassalized, Osraige was typically a subject of the kings of Munster, not Leinster (despite being in the modern 'province' of Leinster). It was counties Laois and Kilkenny, ruled by Cerball mac Dúnlainge, easily one of the most powerful men in Ireland.
Osraige is very strange. Ireland possessed about 150 'tuatha', or tribes, usually covering a relatively small area, and kingdoms had numerous tribes inhabiting them. Osraige, however, only had a single actual tribe inhabiting the whole kingdom (though, like all of the tuatha, it had many clans and septs; the smaller family divisions of the tribes). The capitol of the kingdom was actually originally a monastic settlement, Cill Chainnigh/Cill Chainnech, modern Kilkenny; a fortified hill and village built around a church built by St. Canice (his proper Irish name would've been Cainnech). Its king at the time, Cerball, is especially odd these days because the founding Icelandic families, of all people, claimed descent from him, a Gael. In his time though, he was constantly beset by Laigin, Muma (Munster), Brega, and, off-and-on, the Dubliners (and their associated Norse/Danish colonists from Wicklow, Wexford, etc.), who were also, at times, some of his most valued allies. Despite being relatively small in land area controlled, Osraige was extremely resilient, with excellent soldiers, and Cerball was notably a remarkably skilled military leader, as well as diplomat, which is what kept Osraige from being conquered.
The other main kings at the time;
The kingdom of Leinster, Laigin, was unified under the king Dúnlaing mac Muiredach.
The kingdom of Munster, Muma, was under Cenn Fáelad hua Mugthigirn, of the Eoghanachta, 'Cenn Fáelad, grandson of Mugtigern'.
The kingdom of Connacht, already mentioned above, Mugron mac Máel Cothaid. Also, Connaught is a later, now rarely used English spelling. The proper Irish name (and what is now more often used in English than Connaught is anymore) is Connacht.
Two other notables in Ireland;
Tuilelaith ingen Uargalaig - The abbot of Cill-Dara, Kildare Abbey, and effectively chief of the surrounding area.
Féthgno mac Nechtain - The bishop of Ard Macha, Armagh, a vassal of Aed Findliath. The abbots or bishops of Ard Macha held enormous amounts of power in Ireland. One should also mind that Gaelic monastaries and religious communities maintained their own bodies of soldiers, and Gaelic clergy fought in combat regularly the same as other Gaelic freemen and nobles.
Low-ranking members of clans or tribes and low-ranking soldiers would wear leggings and a shirt, sometimes a fur cloak, little if any armor (except a leather vest/waistcoat), and mostly used spears, cudgels, axes, slings, and javelins. Archers in Gaelic society at the time were the Saiogdear (from the Latin term 'Saggitarius'), and were mostly low-ranking soldiers (but not just levied tribesmen) who carried bows to fire off shots before they joined a charge or flanking manuever. Scouting horsemen would also be among these people. The best soldiers from these ranks were low-ranking soldiers hoping to join the professional soldiers; they'd sometimes own indigenous Gaelic swords, which were about two feet long; really they were more like very long knives. Most were double-edged, some had only a single edge, imitating Saxon scramasax. Such 'swords' were very common, usually low quality, but with a sharp edge and point.
Regular soldiers (cliarthaire), nobles (aire/arras), and 'middle-class' freemen didn't wear trousers or leggings at the time, and instead exposed their legs, though may have at times wrapped their legs. They wore a knee-length shirt (some nobles also wore longer robes), with a cloak or sash with plaid, checkers, or stripes on it, in a number of colors displaying their rank (it had nothing at all to do with what clan they belonged to; that usage of plaid is only from the late 1700s or sometime up to the mid 1800s, though I want to touch on this more in a second). The more colors (and darker colors), the higher ranking the wearer is. Shoes, boots that came to about mid-calf, or walking barefoot are all acceptably appropriate. Soldiers in this rank would wear a padded jacket often, but not always, leather caps, the nobles and wealthier ignoble soldiers would have iron round helmets, and scale or mail coats; scale would be made in Ireland, the mail was imported from the vikings, looted off them, or made as imitation, and called Luireach. Gaelic horsemen were mostly middle class soldiers, but there were some mounted noblemen. However, the apex of Gaelic cavalry was still a few centuries off. Spears, javelins, a lot of those, but also, footmen would often carry axes (both native Gaelic axes, and Norse imports/loot/copies) and native Gaelic shortswords. The wealthy (nobles, called the 'Arras', heroes, called the 'Curadh', and the bodyguards of nobles, 'Deaisbard') would use longer, better quality native Gaelic swords (which were outgrowths of ancient Celtic longswords, but had their own art style to them), as well as, if they could afford them, or get them off the dead, viking swords, which were highly prized.
Native Gaelic shields were predominantly round, square, or rectangular, leather-covered, not very large, and not usually decorated (or at least not decorated very complex), but Norse-style shields also saw use in regions nearest viking influence. Gaels, like vikings, fought in shieldwalls, but supported them with some cavalry (most of which was meant to throw their missiles, skirmish a bit, and chase down routers, or throw their missiles to disorient the enemy formation, and then dismount to fight in the melee) and huge amounts of short range missiles (javelins and darts carried by practically every soldier, from random tribesmen up to nobles).
Obviously, no kilts, they wouldn't exist for centuries more, and wouldn't be popular till nearly two centuries after their invention anyway. Gaelic spears were kind of short, usually, but there were longer spears as well (gaesum), and pikes (geadus). Javelins had numerous variants; the extremes are the half-length javelin, or dart, which had flights on it like an arrow, and the short spear-length 'throwing spear', and, in between, various lengths of javelin. Further, harpoons and slings would be employed at range.
Sources are Early Medieval Ireland 400-1200 by Daibhi O Croinin, The MacMillan Atlas of Irish History, Irish Kings and High Kings, The Peoples of Ireland from Prehistory to Modern Times, and Richard Hayes 11 volume Manuscript Sources for the History of Irish Civilization.
And a bit of art I found on a forum, and have reposted elsewhere, but imagine it'd be useful for illustrating my point, though neck torcs had fallen into disuse most likely.
![[BRE] Louen Leoncœur](/data/avatars/s/412/412944.jpg?1605051629){kind=avatar}