Kleerup began his music career as a songwriter, going on to tour with Teddybears and Robyn.

Kleerup's self-titled debut album, released in 2008, featured collaborators such as Lykke Li, Robyn, and Neneh Cherry.

He received six Grammis nominations for the album, winning in the "Best Newcomer", "Best Producer", and "Best Composer" categories.

In 2010, he and Carl Bagge composed the music for Stockholm City Theatre's 50th-anniversary performance, a musical adaptation of Nobel Prize laureate Harry Martinson's Aniara, performed by a double string quartet.

[1] In September 2014, Kleerup announced the first of two mini-LPs, As If We Never Won,[2] and shared credit of the song "Let Me In" with Susanne Sundfør.