Stapleton was a distinguished centre forward, once touted as being amongst the best in the world in his position, who was an exceptionally strong header of the ball. He started his career with Arsenal, joining them in 1972 as an apprentice, after being turned down by Manchester United. He made his first-team debut in March 1975, at home to Stoke City, and would go on to form a potent striking partnership with Malcolm Macdonald; the two scored 46 goals between them in 1976–77. He was Arsenal's top scorer for the three following seasons, and helped the Gunners reach a trio of FA Cup finals; Stapleton scored one of the goals in Arsenal's 1979 FA Cup Final 3–2 win over Manchester United, and scored 108 goals in 300 appearances in total for the Gunners.