In this work, the parameters of antireflection interference coatings based on alternating layers of ZnS/Al2O3 on the laser-induced damage threshold (LIDT) of ZGP crystals under the action of Ho:YAG laser radiation at a wavelength of 2.097 μm were determined. The coating deposition was carried out using the ion-beam sputtering method. The LIDT of the sample with a coating based on alternating layers ZnS and Al2O3 was equal to WoE = 3.45 J/cm2, and the LIDT of the uncoated sample was equal to WoE = 2.23 J/cm2. An increase in the optical breakdown threshold by ~55% was observed after the deposition of an AR coating based on ZnS and Al2O3 materials. An assumption was made about the absence of local fluctuations in the composition and mechanical stresses in the case of the coated sample, namely that this leads to good adhesion of the multilayer coating to the polished surface of the crystal, and as a result to an increase in the optical breakdown threshold as compared to the uncoated sample due to closure of the dangling chemical bonds and bulk defects emerging on the polished surface.