Clempson began his career in the late 1960s with the power trio, Bakerloo (originally The Bakerloo Blues Line), playing blues-rock. In 1969, he joined Colosseum, until they disbanded in 1971, but re-joined to form a reunion version of the band in 1994, and has continued to perform with them since that time. After Colosseum's split he went on to join Humble Pie in 1971, replacing Peter Frampton. When the band split in 1975 he and Greg Ridley joined drummer Cozy Powell to form Strange Brew. During this period, Clempson auditioned for Deep Purple but lost to Tommy Bolin.
Clempson has appeared as a guest musician with Jack Bruce, Billy Cobham and Dave Sancious, Pink Floyd's Roger Waters, Manfred Mann's Earth Band, Bob Dylan, Chris de Burgh and Jon Anderson.
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