Background
He was the son of William Annesley, 1st Viscount Glerawly and Lady Anne Beresford, the daughter of Marcus Beresford, 1st Earl of Tyrone.
He was the son of William Annesley, 1st Viscount Glerawly and Lady Anne Beresford, the daughter of Marcus Beresford, 1st Earl of Tyrone.
On 12 September 1770 he succeeded his father as Viscount Glerawly and assumed his seat in the Irish House of Lords. On 17 August 1789, Annesley was created Earl Annesley, of Castlewellan in the County of Down, in the Peerage of Ireland.
He held the office of Member of Parliament for Downpatrick between 1761 and 1770.