Constant began his first-class cricket career with Kent in 1961 before moving to Leicestershire in 1965 and playing there until 1968. He was a middle-order batsman who made 67 first-class appearances.
Constant's professional cricket career began with Kent in 1961, followed by a stint at Leicestershire from 1965 to 1968.  He played as a middle-order batsman and made 67 appearances in first-class matches.