Burton's military career began in the 2nd Troop of Horse Grenadier Guards, where he rose to the rank of Major, serving under George Augustus Eliott, the defender of Gibraltar. In 1754, Burton was appointed Lieutenant Colonel of the 48th Foot, which was involved in the captures of Quebec in 1759 and Martinique and Havanna in 1762. In 1760, General Jeffery Amherst, Governor General of British North America, appointed him lieutenant governor of the Trois-Rivières district while New France remained under British military rule.