Background
Moore was the eldest surviving son of Stephen Moore, 1st Viscount Mount Cashell, by Alicia Colville, daughter of Hugh Colville.
Moore was the eldest surviving son of Stephen Moore, 1st Viscount Mount Cashell, by Alicia Colville, daughter of Hugh Colville.
He was returned to the Irish House of Commons for Lismore, a seat he held until 1766, when he succeeded his father in the viscountcy and entered the Irish House of Lords. In 1781 he was created Earl Mount Cashell, of Cashell in the County of Tipperary, in the Irish peerage. In 1785 he was also sworn of the Irish Privy Council.
Lord Mount Cashell married Lady Helena Rawdon, daughter of John Rawdon, 1st Earl of Moira, in 1769.
They had several children. One daughter, Lady Helena Moore, married George King, 3rd Earl of Kingston, and was the mother of antiquarian Edward King, Viscount Kingsborough.