The Kingdom of Laithlind also controls territory in Ireland but that is a Norse kingdom, not a Gaelic one.
Like the Brittonic areas, the Gaelic countries rarely come into play in the main storyline. However, with the exception of Laithlind, all Irish factions are decently strong when it comes to war with other factions.
The Gaels have been in Ireland for thousands of years, and had never broken to invaders. During the Roman Era in British History, the Gaels never thought of conquering the Roman lands as they were much stronger than them. After the collapse of the Roman Empire and the subsequent retreat of the Roman administration and army from Britain, the Gaels, along with the Picts, begun raiding Britain. These raids were ultimately stopped by Anglo-Saxon mercenaries hired by King Vortigern for this express purpose, with the added side effect that this eventually triggered the Anglo-Saxon settlement of Britain. Although prevented from conquering Britain, the Gaels did not completely stop their raids on the island. In particular, Gaelic raiders begun settling in Scotland, and ultimately merged with the Picts to create the Kingdom of Alban.