Conn is the son of the footballer Alfie Conn Sr., who was one of the ‘Terrible Trio’ of Heart of Midlothian in the 1950s.
Conn made his senior debut for Rangers against Dundalk in the Fairs Cup tournament in November 1968. He was part of the Rangers team which lifted the European Cup Winners’ Cup in 1972 and also helped the Ibrox team win the Scottish Cup in 1973, scoring their second goal in a 3â2 final victory over Celtic at Hampden Park.