She was elected to the Norwegian Parliament from Oslo in 1989, but was not re-elected in 1993. She had previously served as a deputy representative during the term 1985–1989.
From 2001 to 2005, when the second cabinet Bondevik held office, Clemet was Minister of Education and Research. As Minister of Education and Research, Clemet became known for her work in carrying out "The Quality Reform" (Kvalitetsreformen) in the Norwegian university system.
Clemet lives together with party fellow Michael Tetzschner; they have two children. Her father Fridtjov Clemet was general secretary of the Conservative Party from 1975 to 1985.