Clemence is best known as part of the Liverpool team from 1967 to 1984. He started his career with Scunthorpe United. He was signed by Liverpool manager Bill Shankly in June 1967. He won five league titles, two domestic cups, two UEFA Cups, three European Cups and other trophies with Liverpool. His final game for Liverpool was in the side's 1–0 win in the 1981 European Cup Final against Real Madrid. He then played for Tottenham Hotspur. He won three trophies with Tottenham, including an FA Cup and a UEFA Cup.