From the Wikipedia page 
Alexander Plunket ( died 1503 ) was appointed Lord Chancellor of Ireland by King Henry VII of England in 1492. Lord Portlester was Lord Chancellor and Lord Treasurer of Ireland before Plunket. The offices were split between Alexander Plunket and Sir James Ormond, who became Lord Treasurer of Ireland. Ireland was in great conflict at this time, as Henry VII tried to get the Irish to pledge loyalty to him, instead of their own Kings and Princes. O'Flanagan states that it is impossible to judge his career as Chancellor since no record of his judgments exist.
He was born in County Meath, son of Sir Thomas Plunket, Lord Chief Justice of the King's Bench in Ireland;he was a close relative of another Sir Thomas Plunket who became Chief Baron of the Irish Exchequer. Through his three marriages he had close connections to both the Earl of Kildare and the Earl of Ormonde; his political loyalties were with the Kildare faction though he later quarreled with them.He was a companion of the Order of Saint George, and served as Sheriff of Meath in 1482. So long as the House of York reigned he appears to have been a loyal enough Yorkist; he was at Court in 1479 and in 1484 received a letter from Richard III thanking him for his services. Henry VII, however trusted him enough to make him Chancellor; this was apparently an effort to curb the power of the Fitzgeralds, with whom Plunket had quarreled. ]He left office in 1494 and died in 1503