  Layered transition metal dichalcogenides have rich phase diagram and they
feature two dimensionality on numerous physical properties. Co1/3NbS2 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 Co1/3NbS2 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,
Co1/3NbS2 displays a different orbital character near the Fermi level compared
to the pristine NbS2 compound and has a clear band dispersion in kz direction
despite its layered structure. Our photoemission study demonstrates the
out-of-plane electronic correlations introduced by the Co intercalation, thus
offering a new perspective on this compound. Finally, we propose how Fermi
level tuning could lead to exotic phases such as spin density wave instability.
