Using angle-resolved photoemission spectroscopy (ARPES) with spin resolution, scanning tunneling microscopy/spectroscopy (STM/STS) and density functional theory (DFT) methods, we study the electronic structure of graphene-covered and bare Au/Co(0001) systems and reveal intriguing features, arising from the ferrimagnetic order in graphene and the underlying gold monolayer. In particular, a spin-polarized Dirac-cone-like state, intrinsically related to the induced magnetization of Au, was discovered at point. We have obtained a good agreement between experiment and theory for bare and graphene-covered Au/Co(0001) and have proven that both Au ferrimagnetism and the Dirac-cone-like band are intimately linked to the triangular loop dislocations present at the Au/Co interface. STM measurements and simulation of the local density of states reveal a magnetic band gap in the electronic structure of graphene for out-of-plane magnetization. This gap is promising for achieving a quantum anomalous Hall state in graphene.