Preserving consistency properties, such as preventing forwarding loops, black-holes, and congestion, is crucial during the transitions in network forwarding state that occur between network updates. Nevertheless, maintaining these properties within SDN networks poses challenges due to flexibility and programmability of SDN, which can result in an increased frequency of network updates. While existing research has introduced mechanisms to uphold consistency during network transitions, they often overlook the consideration of flow priority when scheduling forwarding rules. We address this problem with pUpdate, a framework designed to facilitate consistent and continuous network updates while accounting for flow priority in the scheduling of forwarding rules within SDN. We have developed pUpdate and rigorously evaluated its performance through simulations. The measurements demonstrate that pUpdate adheres to priority-based scheduling without any degradation in network update performance when compared to state-of-the-art approaches in SDN network update.