Jeremiah Clarke (c.1674 - 1707) was a pupil of John Blow at St Paul's Cathedral and a chorister in 1685 at the Chapel Royal. Between 1692 and 1695 he was an organist at Winchester College, then between 1699 and 1704 he was an organist at St Paul's Cathedral. He later became an organist and 'Gentleman extraordinary' at the Chapel Royal, he shared that post with fellow composer William Croft, his friend. They were succeeded by John Blow.

Today, Clarke is best remembered for a popular keyboard piece that was originally either a harpsichord piece or a work for wind ensemble: the Prince of Denmark's March, which is commonly called the Trumpet Voluntary, written in about 1700.

From c. 1878 until the 1940s the work was attributed to Henry Purcell, and was published as Trumpet Voluntary by Henry Purcell in William Spark's Short Pieces for the Organ, Book VII, No. 1 (London, Ashdown and Parry). This version came to the attention of Sir Henry J. Wood, who made two orchestral transcriptions of it, both of which were recorded. The recordings further cemented the erroneous notion that the original piece was by Purcell. Clarke's piece is a popular choice for wedding music, and has been used in royal weddings.

The oldest source of this piece is A Choice Collection of Ayres, a collection of keyboard pieces published in 1700. A contemporary version for wind instruments also survives. According to some sources, the march was written in honour of Prince George of Denmark, husband of Queen Anne of Great Britain.