[1] Klenskaja was born in Tartu, of Russian parentage.
[2] From 1968 until 1970, she worked in the Estonian State Youth Theatre in Tallinn as a make-up artist and in the prop department.
In 1974 she graduated from the Tallinn State Conservatory's Performing Arts Department.
[1] Klenskaja was in a relationship with actor Aarne Üksküla for over thirty years, until his death in 2017.
[2][3] Klenskaja died on 6 January 2022, aged 70, following a prolonged illness.