Tune-Hansen began his career in his hometown club Holbæk B&I, where he scored six goals in 64 games between 1972 and 1976.[2]
Ahead of the 1976–77 2. Bundesliga season, Tune-Hansen moved to FC St. Pauli.[3] He made his debut on 14 August 1975 in the 1–0 defeat by Wuppertaler SV, and scored his first goal in the game in a 1–1 draw against 1. SC Göttingen 05.[4] Tune-Hansen becamea regular starter, played all 38 games and scoring eight goals. At the end of the season his team won promotion to the Bundesliga.[5][6]
Tune-Hansen played his first Bundesliga game on the first matchday in a 3–1 win over Werder Bremen. At the end of the 1977–78 season, his club suffered direct relegation. That season, Tune-Hansen had scored one goal in 33 Bundesliga appearances, which was against Bayern Munich,[7] but he also scored an own goal in the 4–0 defeat against 1. FC Saarbrücken.[8]
After another season in the jersey of the St. Pauli, Tune-Hansen left the club after the club did not receive a license and was therefore relocated to the Oberliga Nord.[9] He signed with VfL Osnabrück for the 1979–80 season.[10] He made his debut on the first matchday of the season against SV Arminia Hannover (2–0 loss).[11] There, too, he became a regular starter, and left the club after three years where they had finished in midtable in the 2. Bundesliga. His departure also marked the end of a six-year stint in Germany with 220 games and 27 goals. He then returned to hometown club Holbæk B&I.[2]
After three more years in Holbæk, Tune-Hansen ended his active career in the 1985 season in Denmark.[2]