Layered transition metal dichalcogenides have a rich phase diagram and they feature two-dimensionality in numerous physical properties. Co_1/3NbS₂ is one of the newest members of this family where Co atoms are intercalated into the van der Waals gaps between NbS₂ layers. We study the three-dimensional electronic band structure of Co_1/3NbS₂ using both surface and bulk sensitive angle-resolved photoemission spectroscopy. We show that the electronic bands do not fit into the rigid band shift picture after the Co intercalation. Instead, Co_1/3NbS₂ displays a different orbital character near the Fermi level compared to the pristine NbS₂ compound and has a clear band dispersion in the k_z direction despite its layered structure. Our photoemission study demonstrates the out-of-plane electronic correlations introduced by the Co intercalation, thus offering a different perspective on this compound. Finally, we propose how Fermi level tuning could lead to exotic phases such as spin density wave instability.