Kleive put 1972 Kantor exam at the Conservatory of Oslo from 1973 to 1976 and studied organ at the Staatliche Hochschule für Musik in Munich. He worked then as an organist at various churches, since 1987 at the Helgerud Kirke in Bærum.
As a concert organist Kleive debuted in 1987 in Oslo. He performed at numerous festivals and organ as soloist with the Kringkastingsorkesteret, the Stavanger Symphony Orchestra and the Trondheim Symphony Orchestra. In 1992 he undertook with the Oslo Filharmoniske Orkester under Mariss Jansons as synthesizer player a tour of the UK.
After Kleive had collected during his studies as a singer of the Munich Bach Choir under Karl Richter experience of choral music, he founded in 1988 the Oslo Bach -kor, which he has since then.
In addition to his work as a classical musician Kleive is also active in the field of jazz and folk music. Since 1972 he has participated in over 200 recordings as a studio musician, arranger or composer. He was a sideman for musicians like Arve Tellefsen, Karin Krog, Jan Garbarek and Terje Rypdal, undertook in 1990 a U.S. tour with Ole Edvard Antonsen, played with Bjørn Eidsvåg in Moscow, with the Ytre Suløens Jassensemble in New Orleans and with Sigmund Groven in Scotland, the United States and the Caribbean. Knut Reiersrud he undertook a tour of India, Pakistan and South Africa.
In 1992 he received the Spellemannprisen for album Blå Koral by Knut Reiersrud. In 1995 he published Kyrie, his first CD with his own compositions. 1995 be Juleevangeliet with the Oslo Bach Choir and the soloists Paolo Vinaccia, Jon Eikemo, Anne Gravir and Ronnie Johansen was premiered.
2007 completed Kleive his Requiem for chorus, soloists and organ, which he recorded in the same year in Ljubljana as an organist with the Oslo Bach Choir, the Chamber Choir Mimas Tromsø, the choir APZ Tone Tomsic from Ljubljana and the soloist Marianne E. Andersen and Trond Hallstein Moe. In 2008 he played on the organ music for the Norwegian film Troubled Water.
- Max Reger: Inferno, 1988
- Blå in coral ( with Knut Reiersrud ), 1991
- Max Reger: All men must die, 1993
- Kyrie, 1994
- Skip sky ( with Knut Reiersrud ), 1996
- Juleevangeliet, 1998
- The signede dag ( with Knut Reiersrud and Povl Dissing ), 2000
- Hyrdenes tilbedelse, 2004
- Julemeditasjoner ( with Aage Kvalbein ), 2007
- Requiem, 2007
- Som the gylne sol ( with Iver Kleive and Povl Dissing ), 2013
- Classic pianist
- Classic organist
- Norwegian composer
- Born in 1949