The formation of an Electron Cloud (EC) in the vacuum chambers could significantly limit the performances of the positron damping ring of the Compact Linear Collider (CLIC). Depending on the Secondary Electron Yield (SEY) of the inner surface of the vacuum chambers, electrons generated by photoemission due to synchrotron radiation, can multiply through beam induced multipacting and accumulate in the chamber. The high electron flux on the chamber’s wall can lead to important heat loads on the cold wigglers and degrade the vacuum quality all along the ring due to electron simulated desorption. Moreover, the high electron density in the vacuum chamber can induce coherent and incoherent effects on the beam (e.g. instabilities, emittance blow up). A PyECLOUD simulation campaign has been carried out in order to characterize the EC build up in the different components of the ring (dipole, quadrupole and wiggler magnets) and provide specifications for suitable mitigation strategies, like low SEY coatings and/or clearing electrodes.