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M_rM’X₂ (with M = V, Cr, Mn, Fe, Co, Ni; M’ = Nb, Ta; X = S, Se; r = 1/3, 1/4) are layered materials in which M atoms are intercalated in the van der Waals gaps between M’X₂ layers, exhibiting interesting structural and magnetic properties. Here we investigate the electronic structure of Cr_1/3TaS₂ using first-principles methods based on a combination of density functional theory and embedded dynamical mean field theory, partly motivated by recent experimental observations of unusual optical responses. We find that the system has localized orbitals in Cr 3d states as well as itinerant ones in Cr 3d and Ta 5d, where the metallic states with small scattering rates indicate a conventional Fermi liquid. The possibility of inducing an orbital-selective Mott transition is also explored. We further investigate the optical conductivity to examine the origin of the experimentally observed optical changes. Our study is important for the theoretical understanding of the electronic structure and the optical properties of Cr_1/3TaS₂.