The son of a Yorkshire farmer, Clappison was born in Beverley, East Riding of Yorkshire and educated at the independent St Peter's School, York, before attending The Queen's College, Oxford where he graduated with a Bachelor of Arts degree in Philosophy, Politics and Economics in 1978.
Clappison married Helen Margherita Carter in July 1984 in Leeds and they have a son (born in March 1987) and three daughters (born April 1985, August 1989 and April 1995).