Born the younger son of Simon Harcourt, 1st Earl Harcourt and Rebecca Harcourt ("née" Samborne Le Bas), Harcourt was commissioned as an ensign in the First Regiment of Foot Guards on 10 August 1759. He became a captain in the 16th Light Dragoons, a regiment which had been raised at his father's expense and was known as "Harcourt's Black Horse", on 27 October 1759. He transferred to the 3rd Dragoons on 30 June 1760 and was subsequently sent to Mecklenburg-Strelitz (with his father) to escort the consort-elect of King George III to England. In recognition of this mission he was appointed an equerry to the Queen Consort later that year.