The Compact Linear Collider (CLIC) is a mature option for the future of high energy physics. It combines the benefits of the clean environment of $e^+e^-$ colliders with operation at high centre-of-mass energies, allowing to probe scales beyond the reach of the Large Hadron Collider (LHC) for many scenarios of new physics. This places the CLIC project at a privileged spot in between the precision and energy frontiers, with capabilities that will significantly extend knowledge on both fronts at the end of the LHC era. In this report we review and revisit the potential of CLIC to search, directly and indirectly, for physics beyond the Standard Model.