Edling started his musical career in the band Trilogy, then under the name of Toxic, as a singer together with Ian Haugland (later the drummer of Europe) in 1979. He then played in a band named Witchcraft but left in 1981 and formed Nemesis in 1982. Before the Candlemass official releases, Edling also handled vocal duties in addition to playing bass.
After the departure of Messiah Marcolin, Candlemass became his solo project, until the band reformed in 2002. In 1994, when Candlemass fell apart, Leif had started the band Abstrakt Algebra with Mats Levén on vocals and Mike Wead on guitar. The band met with limited success and split up after one album.
In 2002 he founded another doom metal band, named Krux, also with Mats Levén on vocals, and in 2013 founded Avatarium with Marcus Jidell on guitar and Jidell's wife, Jennie-Ann Smith on vocals.