He made his debut in a 1–0 win over Chelsea on 25 December 1954, and by the end of the 1954-55 he was Arsenal's first choice right-winger, taking Arthur Milton's place.
Clapton was also called up for England, playing a solitary international match against Wales on 26 November 1958 at Villa Park, which finished 2-2.
After Arsenal signed Jackie Henderson and Alan Skirton, Clapton had to be content with sharing the right wing position in 1959-60 and 1960-61.
Arsenal then signed Johnny MacLeod in the summer of 1961, and Clapton lost his place in the side altogether (only playing five matches in 1961-62) and was sold to Luton Town in September 1962.
His younger brother Denis was also a footballer, but never achieved the same success, making only five league appearances for Arsenal and Northampton Town.