Career
He was educated at the University of Cambridge. Annesley succeeded in the earldom in August 1838 on the death of his father. As this was a title in the Peerage of Ireland it did not entitle him to a seat in the House of Lords.
He was instead elected to the House of Commons for Great Grimsby in the 1852 general election, a seat he held until 1857.
In 1867 he was elected an Irish Representative Peer, which he remained until his death.