The field of energy, specifically renewable energy sources (RES), is considered vital for a sustainable society, a fact that is clearly defined by the European Green Deal. It will convert the old, conventional economy into a new, sustainable economy that is environmentally sound, economically viable, and socially responsible. Therefore, there is a need for quick actions by everyone who wants to move toward energy-efficient development and new environmentally friendly behavior. This can be achieved by setting specific guidelines of how to proceed, where to start, and what knowledge is needed to implement such plans and initiatives. This paper seeks to contribute to this very important issue by appraising the ability of full-scale implementation of RES combined with energy storage in an island power system. The Greek island power system of Astypalaia is used as a case study where a battery energy storage system (BESS), along with wind turbines (WTs), is examined to be installed as part of a hybrid power plant (HPP). The simulation’s results showed that the utilization of HPP can significantly increase RES penetration in parallel with remarkable fuel cost savings. Finally, the fast response of BESS can enhance the stability of the system in the case of disturbances.