We study the galaxy mass-size relation in 15 spectroscopically confirmed clusters at 1.4 < z < 2.8 from the CARLA survey. Our clusters span a total stellar mass in the range 11.3 < log(M c * /M ) < 12.6 (with an approximate halo mass in the range 13.5 log(M c h /M ) 14.5). Our main finding is that cluster passive early-type galaxies (ETGs) at z 1.5 with a mass log(M/M ) > 10.5 are systematically 0.2−0.3dex larger ( 3σ) than field ETGs at a similar redshift and mass from the CANDELS survey. The passive ETG average size evolution with redshift is slower at 1 < z < 2 when compared to the field. This could be explained by early-epoch differences in the formation and early evolution of galaxies in haloes of a different mass, as predicted by models. It does not exclude that other physical mechanisms, such as strong compaction and gas dissipation in field galaxies, followed by a sequence of mergers may have also played a significant role in the field ETG evolution, but not necessarily in the evolution of cluster galaxies. Our passive ETG mass-size relation shows a tendency to flatten at 9.6 < log(M/M ) < 10.5, where the average size is log(R e /kpc) = 0.05 ± 0.22, which is broadly consistent with galaxy sizes in the field and in the local Universe. This implies that galaxies in the low end of the mass-size relation do not evolve much from z ∼ 2 to the present, and that their sizes evolve in a similar way in clusters and in the field. Brightest cluster galaxies lie on the same mass-size relation as satellites, suggesting that their size evolution is not different from satellites at redshift z 2. Half of the active early-type galaxies, which are 30% of our ETG sample, follow the field passive galaxy mass-size relation, and the other half follow the field active galaxy mass-size relation. These galaxies likely went through a recent merger or neighbor galaxy interaction, and would most probably quench at a later epoch and increase the fraction of passive ETGs in clusters. We do not observe a large population of compact galaxies (only one), as is observed in the field at these redshifts, implying that the galaxies in our clusters are not observed in an epoch close to their compaction.