The large scale particle accelerators of the future in the 20 T regime are enabled by high temperature superconducting magnets. The dipole magnets needed in new high-field accelerators can be constructed with an YBCO insert and a Nb3Sn outsert. Such a configuration makes the quench analysis and magnet protection challenging because the quench behavior in both of these coils is different and there is very strong inductive coupling between the coils. The Nb3Sn coil is characterized by high energy and current and relatively fast quench propagation velocity. However, quench propagates slowly in YBCO coils because of typically wide spread large temperature margin. Currently, in the EuCARD project, a European collaboration is targeting to construct a small-scale high field YBCO-Nb3Sn hybrid magnet. In this paper, we scrutinize quench in the YBCO insert. We utilized an approach based on a solution of the heat diffusion equation with the finite element method. Additionally, we present a protection scheme for the coil.