Crosbie was the son of Maurice Crosbie, 1st Baron Brandon, by Lady Elizabeth Anne, daughter of Thomas FitzMaurice, 1st Earl of Kerry.
[2] He was returned to the Irish House of Commons for Ardfert in 1735, a seat he held until 1762, when he succeeded his father in the barony and entered the Irish House of Lords.
He married firstly Lady Theodosia, daughter of John Bligh, 1st Earl of Darnley and Theodosia Bligh, 10th Baroness Clifton, in 1745.
After her death in May 1777 he married secondly Jane, daughter of Edward Vesey and widow of John Ward, in 1777, six months after his first wife died.
He died in April 1781 and was succeeded in the earldom by his only surviving son from his first marriage, John.