He was educated at the University of Edinburgh, Göttingen and Berlin.
He was called to the bar at Lincoln"s Inn in 1833, but later moved to the Middle Temple. He went on the Northern circuit. He was elected in 1857 but lost the seat in 1859.
At the 1868 general election Stapleton was re-elected for Berwick and held the seat until his defeat at the 1874.
Stapleton died at the age of 75. Stapleton married Frances Dorothea King, second daughter of Edward Bolton King, of Chadshunt, Warwickshire.
16th United Kingdom Parliament. 17th United Kingdom Parliament. 20th United Kingdom Parliament]
At the 1852 general election, Stapleton was elected as a Member of Parliament (Member of Parliament) for Berwick upon Tweed but was unseated on petition.