Klæstrup was born in 1994, the daughter of a Social Democratic father and a mother who was a former member of the Red-Green Alliance. She comes from the Guldborgsund Municipality. Klæstrup is a student from Vordingborg Gymnasium and HF, and is now a rhetoric student at the University of Copenhagen.
Klæstrup was a member of the Young Conservatives until 2015. She ran for the Conservative People's Party in the Danish local elections in 2013 for the council in Guldborgsund Municipality. She received 128 personal votes, but was not elected. Klæstrup changed to the Liberal Alliance after the general election in 2015.
Klæstrup has worked as a fashion model for several years, including topless pictures. The combination of her political work and her physical appearance has secured her a lot of media publicity. The first time she received attention was during the Municipal elections in 2013, when she won a competition for This year's election babe held by the tabloid newspaper Ekstra Bladet.
