He was the son of David Crosbie, High Sheriff of Kerry, and his wife Jane Hamilton, daughter of William Hamilton of Lisclooney, County Offaly, and grandson of Sir Thomas Crosbie, also High Sheriff of Kerry, and his wife Bridget Tynte.
His father and grandfather both opposed the Glorious Revolution, and thereafter lived quietly on their County Kerry estates; Maurice's election to the House of Commons in 1713 marked the family's return to political prominence.
His descendants became substantial landowners in Kerry: the senior branch of the family ere the Crosbie baronets of Maryborough, the last of whom, Sir Edward Crosbie, was executed for treason as a United Irishman in 1798.
In 1713 he was elected to the Irish House of Commons as the Member of Parliament for County Kerry.
They had seven children, including William Crosbie, 1st Earl of Glandore, Maurice Crosbie, Dean of Limerick, father of the 4th and last Baron Brandon, Mary Ann, who married John Coppinger of Glenville, County Cork and was the mother of the lawyer and politician Maurice Coppinger, Elizabeth, who married her distant cousin Lancelot Crosbie, and Jane, who married Thomas Mahon and was the mother of Maurice Mahon, 1st Baron Hartland.