By means of ab initio density functional theory (DFT) calculations, we examined the surface electronic structure of the TbIr 2 Si 2 antiferromagnet, which is distinguished by the out-of-plane alignment of Tb 4f moments and a high Neel temperature. We analyzed the interplay between the spin-orbit and exchange in- ´ teractions and their effect on the dispersion of surface states resided in the projected band gap around the M¯ point of the surface Brillouin zone, and compared our theoretical findings with low-temperature angle-resolved photoemission spectroscopy (ARPES) measurements.