The earliest thing we really know about Clarke is that he was a boy choir singer in the Chapel Royal at the time of the coronation of James II. His voice changed in 1692; in that year he became the organist of Winchester College. He left there in 1696, and reappears in the record on June 6, 1699, when he was appointed a vicar-choral of St Paul's Cathedral, London. He received some promotions and titles, and in 1704 took the position of organist of the Chapel Royal, jointly with William Croft. He wrote attractive and popular theater pieces, many effective anthems, and other sacred music, and some harpsichord pieces including The Prince of Denmark's March, which is the proper name for the piece of worldwide fame known as the Trumpet Voluntary. (The work itself has an interesting history. Its familiar trumpet, organ, and drum arrangement is of contemporary origin, but was inspired by a nineteenth century organ version that ascribed the tune to Henry Purcell, at the time one of the few names known to posterity from the then-shadowy Baroque era.)
Accounts of Clarke's life suggest that he was subject to periods of deep depression. He shot himself and was buried in the crypt of St. Paul's Cathedral.