General. Gordon was the son of Alexander, 2nd Duke of Gordon (c.1678 - 1728) who entered the army and rose to the rank of general. He attempted to promote the British colonisation of Florida in 1764. In 1767, he married Jane, widow of James Murray, 2nd Duke of Atholl (1690 - 1764).
Gordon was appointed Commander-in-Chief of the army in Scotland (1782) and Governor of Edinburgh Castle (1786).