Stapylton was the eldest son of Sir Henry Stapylton and his wife Elizabeth Darcy, daughter of Conyers Darcy, 1st Earl of Holderness, of Hornby Castle, Yorkshire. His father had been a Member of Parliament during the Commonwealth and was created a baronet shortly after the Restoration in 1660.[1] Stapylton matriculated at Christ Church, Oxford on 3 November 1674, aged 17, and was awarded BA in 1677.[2] He succeeded to the baronetcy and Myton Hall following his father's death on 26 March 1679.
Stapylton was returned as Member of Parliament for Aldborough on the Wentworth interest at the second general election of 1679. He was inactive in the second Exclusion Parliament, and did not stand again until after the Revolution. He married Anne Kaye, daughter of Sir John Kaye, 2nd Baronet of Woodsome on 15 April 1680. In 1683, he became JP for West Yorkshire and served as High Sheriff of Yorkshire for the year 1683 to 1684. He became Deputy Lieutenant of Yorkshire in 1685. In 1688 he was removed from his local offices as JP and DL, but was re-instated in 1689.[3]