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 drummerCozy Powell to form Strange Brew. During this period, Clempson auditioned for Deep Purple but lost to Tommy Bolin. Although he played in Marriott’s All Stars he opted not to join the reformed Humble Pie in 1980.
From 2008 to summer 2012 he played as a member of Hamburg Blues Band. After that he has formed his own The Clem Clempson Band which started touring in the end of February 2013 in Braunschweig, Germany. Among others the band include Adrian Askew from Hamburg Blues Band and the band is featuring also Chris Farlowe in vocals occasionally.