Born in Liverpool, Moore was the son of Charles Moore who had served as Member of Parliament (MP) for Tipperary from 1865 to 1869. He was educated at Ushaw College, Durham. He married Mary Lucy Clifford of Hatherton Hall, Stafford, daughter of Sir Charles Clifford, on 7 February 1877. They resided at Mooresfort, Lattin, County Tipperary, Ireland.
Moore was elected at the 1874 general election as a Home Rule League MP for Clonmel, holding the seat in the Parliament of the United Kingdom until the constituency’s abolition for the 1885 general election. In Parliament he strongly advocated land reform, better treatment of children in workhouses, university education for Irish Catholics, and Home Rule.
He returned to the House of Commons briefly as an Irish Parliamentary Party MP, after winning a by-election on 16 February 1899 for the Londonderry City, but held the seat only until the general election the following year. He also held the offices of Deputy Lieutenant, Justice of the Peace and was High Sheriff in 1877. He was affiliated with the section of the Irish Party led by T.M. Healy and his defeat as MP for Londonderry city in 1900 was partly due to the hostility of the dominant faction led by John Dillon.