Klæstrup was a member of the Young Conservatives until 2015. During her time in that party, she was local association president in Lolland-Falster KU from 2012-2014. 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. Now she is a political commentator and a member of the Liberal Alliance.