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We propose a novel hierarchical frequency and voltage control design for multi-area power system integrated with inverter-based resources (IBRs). The design is based on the idea of prioritizing the use of IBRs over conventional generator-based control in compensating for sudden and unpredicted changes in loads and generations, and thereby mitigate any undesired dynamics in the frequency or the voltage by exploiting their fast actuation time constants. A new sequential optimization problem, referred to as Area Prioritized Power Flow (APPF), is formulated to model this prioritization. It is shown that compared to conventional power flow APPF not only leads to a fairer balance between the dispatch of active and reactive power from the IBRs and the synchronous generators, but also limits the impact of any contingency from spreading out beyond its respective control area, thereby guaranteeing a better collective dynamic performance of the grid. This improvement, however, comes at the cost of adding an extra layer of communication needed for executing APPF in a hierarchical way. Results are validated using simulations of a 9-machine, 6-IBR, 33-bus, 3-area power system model, illustrating how APPF can mitigate a disturbance faster and more efficiently by prioritizing the use of local area-resources. • A new concept of "area-prioritization"-based power flow (APPF) dispatch is proposed to maximize the participation of inverter-based resources (IBRs) in frequency and voltage control. • A hierarchical computation architecture is developed to implement this prioritization. • Implementation steps are showcased via simulation of a 33-bus power system with 9 generators and 6 IBRs. [ABSTRACT FROM AUTHOR]