Ole Thestrup was born in Nibe, North Jutland, on 12 March 1948. He initially had ambitions to become a Guitarist, before turning to acting. He joined Aarhus Theatre aged 25, completing his acting training in 1976. He later also worked at the Royal Danish Theatre in Copenhagen.

Thestrup's early television roles included the comedy series Een stor familie (1982–1983) and the 1986 Christmas calendar show Jul på Slottet, in which Politiken described him as being "perfectly cast".

Thestrup had a history of alcohol abuse, which contributed to his 1988 imprisonment in Canada after he caused disruption on board a FLIGHT, leading to an emergency landing. He gave up alcohol in 1998.

Director Anders Thomas Jensen regularly cast Thestrup in his films, beginning with the Academy Award-winning 1998 short Election Night. He also appeared in Jensen's feature films Flickering Lights (2000), The Green Butchers (2003), Adam's Apples (2005) and Men & Chicken (2015).

In the early 2000s he played the role of the Captain in Robert Wilson's adaptation of the play Woyzeck by Georg Büchner.

He died on 2 February 2018, in his home in Tuse Næs, following a battle with lung cancer which had stalled his acting career in April 2017.