Metal hydrides enable excellent thermal energy storage due to their high energy density, extended storage capability, and cost‐effective operation. A metal hydride‐driven storage system couples two reactors that assist in thermochemical storage using cyclic operation. Metal hydride reactors, operating at both low and high temperatures, serve for the storage of hydrogen and thermal energy, respectively. The integration of efficient thermal energy storage technology is known to enhance the efficiency of solar thermal systems. In this regard, during the peak hours of solar energy, the high‐temperature supply heat can be utilized to store hydrogen gas in the low‐temperature reactor, which simultaneously facilitates energy storage in the high‐temperature reactor. Moreover, the temperature and energy released from the reactors are highly dependent on the pressure of the gas. As a result, installing a compressor between the low and high‐temperature metal hydride reactors can help generate additional outputs, such as a cooling effect. This paper conducts a thermodynamic analysis to assess the system's performance, considering parameters such as thermal storage efficiency, coefficient of performance (COP), and COPCCH (combined cooling and heating based COP). Moreover, the performance analysis was carried out for two cases, that is, high‐temperature titanium hydride (TiH2) and magnesium hydride (MgH2). The results show that MgH2 and TiH2 achieve a maximum COPCCH of 1.08 and 0.9, respectively, and system storage efficiency of 76.15% and 74.34%, respectively. In spite of having lower efficiency than MgH2, the TiH2‐based system has the ability to recover heat at a very high temperature.