He was the son of Sir Maurice Crosbie, who had previously represented County Kerry in the Irish House of Commons for over forty years, and was raised to the peerage as Baron Brandon in 1758.
His marriage to Elizabeth La Touche, daughter of Colonel David La Touche and Lady Cecilia Leeson, was notoriously unhappy, and in 1829 he brought a celebrated action for criminal conversation against William Lamb, 2nd Viscount Melbourne, then Chief Secretary for Ireland, accusing him of adultery with Lady Brandon.
The action failed for lack of evidence, but public opinion was largely on the husband's side.
Melbourne never admitted to the affair, but he did not, as he did in similar cases like that of Caroline Norton, publicly insist on the lady's innocence, although they remained friends.
The fourth Baron and his wife had one daughter Elizabeth Cecilia, who married Henry Galgacus Redhead Yorke, but they had no surviving male issue, and on his death in 1832 the barony became extinct as well.