He was a member of the prominent Burnell family, who were Lords of the Manor of Balgriffin in County Dublin for several generations, and produced several distinguished judges; in Patrick's own generation, his cousin John Burnell was briefly Chief Baron of the Irish Exchequer.
He is first heard of in 1467, when he was serving as a clerk in the Exchequer of Ireland; in 1477 he was giving evidence to the English Court of Chancery.
In 1478 he was appointed third Baron of the Court of Exchequer (Ireland), following the death of Nicholas Sutton, whose widow, Anne Cusacke, Burnell later married.
He was made Chief Chamberlain as well as a Baron of the Exchequer in 1484, and owned several properties in Dublin, including houses in Fishamble Street.
When Simnel's cause was crushed at the Battle of Stoke Field, the victorious King Henry VII showed remarkable clemency to the rebels (including Simnel himself, who became a servant in the Royal household), and Burnell benefitted from the general royal pardon issued in 1488.