Thermal and mechanical energy storage is pivotal for the effective exploitation of renewable energy sources, thus fostering the transition to a sustainable economy. Hydrogen-based systems are among the most promising solutions for electrical energy storage. However, several technical and economic barriers (e.g., high costs, low energy and power density, advanced material requirements) still hinder the diffusion of such solutions. Similarly, the realization of latent heat storages through phase change materials is particularly attractive because it provides high energy density in addition to allowing for the storage of the heat of fusion at a (nearly) constant temperature. In this paper, we posit the challenge to couple a metal hydride H2 canister with a latent heat storage, in order to improve the overall power density and realize a passive control of the system temperature. A highly flexible numerical solver based on a hybrid Lattice Boltzmann Phase-Field (LB-PF) algorithm is developed to assist the design of the hybrid PCM-MH tank by studying the melting and solidification processes of paraffin-like materials. The present approach is used to model the storage of the heat released by the hydride during the H2 loading process in a phase change material (PCM). The results in terms of Nusselt numbers are used to design an enhanced metal-hydride storage for H2-based energy systems, relevant for a reliable and cost-effective “Hydrogen Economy”. The application of the developed numerical model to the case study demonstrates the feasibility of the posited design. Specifically, the phase change material application significantly increases the heat flux at the metal hydride surface, thus improving the overall system power density.