In his active career, Holmstrøm played the position of striker, guiding Kjøbenhavns Boldklub to two Danish Championships.

He also played professionally for ADO Den Haag and HFC Haarlem in the Netherlands, and French club Girondins de Bordeaux.

In 1969, he moved abroad to play professionally for Dutch clubs ADO Den Haag and HFC Haarlem.

His professional career was quickly over, as he suffered a career-ending injury and was declared medically unfit to play football.

Holmstrøm is well known for his outspoken manners, which had given birth to many classic quotes, which is still cited and loved by the fans of FC Copenhagen today.

"), and "Hellere løve for èn dag, end lænkehund hele livet" ("[I'd] rather be a lion for one day, than a chained dog for one entire life").