According to this article by Adrian Martyn, the last credible claimant to the title of High King of Ireland was a character named Fedlimid Ó Conchobair who took advantage of the Bruce invasion to overthrow the De Burgh (Burke) hegemony in Connacht and aspired to be king of all Ireland.
Unfortunately for him and his followers he was crushed at the battle of Athenry in 1316 by the Burkes, The English and their allies.
What would have happened if medieval Ireland had developed into a Gaelic monarchy? Even more intriguing what if, after a successful Bruce invasion it had been part of a confederated joint Irish Scottish-Gaelic monarchy? (The Bruces were not Gaels by origin but did speak Gaelic and would have been comfortable with the notion).
I speculate not for nationalist reasons (as I'm no fan of monarchies) but just intrigued by how subsequent history could have been so different.