Simpson started his senior career with amateur club Queen's Park; he was selected by their first team in 1945, aged just 14 years and 304 days.
[2] This made him the youngest person to represent a Scottish league club, although it was an unofficial record due to the suspension of normal competitive football during the Second World War.
[2][7] His performances helped to save Hibs from relegation in 1962, but he fell out of favour under the management of Jock Stein due to his attitude in training.
[2] His sense of humour made Simpson a popular figure in the team, who nicknamed him "Faither", on account of his relative old age.
[2] The highlight of his time at Celtic was winning the 1967 European Cup Final, as part of a clean sweep of trophies in the 1966–67 season.
[9][10][11] He suffered a dislocated shoulder in 1969,[2] and trouble with this injury forced him to miss the 1970 European Cup Final and to retire as a player that year.
[2] Simpson also played for the Scotland national team, making his debut in the famous 3–2 win over 1966 World Cup winners England at Wembley in 1967.
[2] He also served on the Pools Panel, which adjudicated on results of postponed matches in periods of exceptionally bad weather.