Born the son of Admiral Sir George Elliot, Elloit was commissioned as a cavalry officer on 22 February 1843. He was promoted to cornet in the 9th Queen's Royal Lancers on 18 July 1848 and to lieutenant in the 5th Dragoon Guards on 14 June 1850. He served as aide-de-camp to General Sir James Scarlett, Commander of the Heavy Brigade, at the Battle of Balaclava in October 1854 during the Crimean War. He went on to command the troops in the North British District in 1885 and retired in 1888.