Born in Edinburgh, Sinclair had an early military career serving in the Sudan with the Royal Irish Lancers. He joined the Liberal Party in the 1880s and was first elected to the London County Council in 1889 as a Progressive Councillor for Finsbury East. He served as Liberal MP for Dumbartonshire (1892-95) and Forfarshire (1897-1909). In parliament Sinclair served as Parliamentary Secretary to Sir Henry Campbell-Bannerman, forming a close political and personal relationship with the future Liberal leader. When Campbell-Bannerman became Prime Minister in 1905 he appointed Sinclair to the cabinet as Secretary of State for Scotland, a post in which he served until 1912. After leaving the cabinet, Sinclair became Governor of Madras until 1919.