Sinclair, an eminent surgeon, was educated at Queen’s College, Belfast, from which he graduated in 1881. He studied in London, Vienna and Berlin and was appointed professor of surgery at Queen’s Medical School in 1886, a position he held for 37 years. Between 1885 and 1939 he was assistant surgeon, attending surgeon and eventually consulting surgeon at the Royal Victoria Hospital. He was also on the staff of the Ulster Hospital for Children and Women. During the First World War he served as consulting surgeon to the Fourth Army. He was awarded the CB in 1917. In addition to his medical career, Sinclair was registrar of Queen’s in 1919 and pro-chancellor in 1931. He was also involved in politics; between 1922 and 1940 he was a member of the senate of Northern Ireland and was MP for Queen’s in the British Parliament (1923–1940).