MSOS (Multiprocessors Synchronization protocol for real-time Open Systems) is a synchronization protocol for handling resource sharing among independently-developed realtime applications (components) on multi-core platforms. MSOS does not consider any priority setting among applications. To handle resource sharing based on the priority of applications, in this paper we propose a new protocol that allows for resource sharing among prioritized real-time applications on a multi-core platform. We propose an optimal priority assignment algorithm which assigns unique priorities to the applications based on information in their interfaces. We have performed experimental evaluations to compare the proposed protocol (called MSOS-Priority) to the existing MSOS as well as to the current state of the art locking protocols under multiprocessor partitioned scheduling, i.e., MPCP, MSRP, FMLP and OMLP. The evaluations show that MSOS-Priority mostly performs significantly better than alternative approaches.