We have investigated the electronic structure of graphene supported on Re(0001) before and after the intercalation of one monolayer of Ag by means of angle-resolved photoemission spectroscopy measurements and density functional theory calculations. The intercalation of Ag reduces the graphene-Re interaction and modifies the electronic band structure of graphene. Although the linear dispersion of the {pi} state of graphene in proximity of the Fermi level highlights a rather weak graphene-noble metal layer interaction, we still observe a significant hybridization between the Ag bands and the {pi} state in lower energy regions. These results demonstrate that covering a surface with a noble metal layer does decouple the electronic states, but still leads to a noticeable change in the electronic structure of graphene.