Clempson, who played as both a forward and a wing half, turned professional with Manchester United in September 1948. He made his debut for the club in 1950 against Sunderland and went on to make 15 league appearances for the club. Eight of these came in 1951–52, when United were champions of England.
In February 1953, Clempson moved to Stockport County, where he played regularly for six years. He was selected to play for the Third Division North representative side in 1954–55. In the summer of 1959, Clempson joined Chester, where his former Manchester United colleague Stan Pearson was manager. Clempson was installed as captain and played for two years before leaving to become player-manager of Hyde United. His signings included his Chester team-mate, Billy Foulkes, who played for Newcastle United and Wales.
