He was born in Kington, Herefordshire, one of 13 siblings and the second son of Roger Kemble and Sarah "Sally Ward". His siblings included Charles Kemble, John Philip Kemble and Sarah Siddons. He and his brothers were raised in their father's Catholic faith; his sisters were raised in their mother's Protestant faith.
George Kemble wed prominent actress Elizabeth Satchell (1783). His niece was the actress and abolitionist Fanny Kemble. His daughter Francis Kemble married Richard Arkwright Jnr's son, Capt. Robert Arkwright. Kemble's son Henry was also an actor.
Similar to his father, Stephen Kemble became a very successful theatre manager of the Eighteenth-Century English stage. He managed the original Theatre Royal, Newcastle for fifteen years (1791–1806). He brought members of his famous acting family and many other actors out of London to Newcastle. Stephen's sister, Sarah Siddons, was the first London actor of repute to break through the prejudice which regarded summer " strolling", or starring in the provincial theatres, as a degradation.
Stephen Kemble guided the Theatre through many celebrated seasons. The Newcastle audience quickly came to regard itself, that is, as "in a position of great theatrical privilege.". The original Theatre Royal was opened on 21 January 1788 and was located on Mosley Street, next to Drury Lane. While in Newcastle upon Tyne Kemble lived in a large house opposite the White Cross in Newgate Street.