A study of the sensitivity of the CLIC ILD detector model for massive long-lived particles produced in the decay of the Higgs boson is presented, using a data sample of $e^+e^-$ collisions at centre-of-mass energy of 350 GeV and 3 TeV, corresponding to an integrated luminosity of 1 ab-1 and 3 ab-1, respectively. The sensitivity range covers long-lived particle lifetimes from 1 to 300 ps, masses between 25 and 50 GeV, and a parent Higgs mass of 126 GeV. Sensitivities to the production cross-section as a function of the long-lived particle mass and lifetime are determined.