Li-containing elpasolite scintillators are currently investigated for their ability to detect both thermal neutrons and gamma photons with a single inorganic crystal. The scintillation is typically triggered by using an activator such as Ce. However, when Tl, also a luminescent ion, is present in the matrix, competition between the two centers Tl and Ce can occur. In this study, we are using Ce doped Tl2LiYCl6 to investigate this competition. To this end, the Ce (which substitutes Y) concentration is varied from 0 to 1 in the Tl2LiY1-xCexCl6 composition. In the low concentration range in which Ce remains a dopant, the photo- and radioluminescence spectra show that the scintillation of Tl2LiYCl6:Ce is mostly dominated by recombination on intrinsic luminescent centers. For cerium concentrations higher than x = 0.02, very different emissions can be easily distinguished from the photo- and radioluminescence of undoped and low Ce doped Tl2LiYCl6 crystals. These emissions are attributed to the formation of a second phase Tl2CeCl5, identified by X-ray diffraction. We conclude that the intrinsic luminescence related to Tl dominates the scintillation in the range of concentration for which Ce does substitute on the Y-site.