His early life is unknown. He was a singer at the Chapel Royal by 1685. He was an organist at Winchester College from 1692 to 1695. He became the vicar-choral of St Paul's Cathedral, London. On 15 May 1704, he became an organist at the Chapel Royal with William Croft. He shot himself on 1 December 1707.
Clarke wrote church music, theatre music, and harpsichord music. His most famous work is the Prince of Denmark's March. It was first published as a harpsichord piece in A Choice Collection of Ayres for the Harpsichord in 1700. It was arranged by Sir Henry Wood in the 19th century for an orchestra. He mistakenly thought that Henry Purcell had composed it. It is often played in weddings and ceremonies.
Another famous piece, the Trumpet Tune in D may have also been written by Clarke. It was also mistakenly thought to have been composed by Henry Purcell. It is a movement from The Island Princess, a set of incidental music. It was written together by Clarke and Daniel Purcell, Henry Purcell's younger brother.
- Powell, Christopher; Johnstone, H. Diack; Shaw, Watkins (2001). "Clarke [Clark, Clerk], Jeremiah (i)". Grove Music Online (8th ed.). Oxford University Press.
- Cudworth, C. L. (1953). "Some New Facts about the Trumpet Voluntary". The Musical Times. 94 (1327): 401–403. doi:10.2307/933069. ISSN 0027-4666.