Peritectic compound Li4(OH)3Br has been recently proposed as phase change material (PCM) for thermal energy storage (TES) applications at approx. 300 °C Compared to competitor PCM materials (e.g., sodium nitrate), the main assets of this compound are high volumetric latent heat storage capacity (>140 kWh/m3) and very low volume changes (<3%) during peritectic reaction and melting. The objective of the present work was to find proper supporting materials able to shape stabilize Li4(OH)3Br during the formation of the melt and after its complete melting, avoiding any leakage and thus obtaining a composite apparently always in the solid state during the charge and discharge of the TES material. Micro-nanoparticles of MgO, Fe2O3, CuO, SiO2 and Al2O3 have been considered as candidate supporting materials combined with the cold-compression route for shape-stabilized composites preparation. The work carried out allowed for the identification of the most promising composite based on MgO nanoparticles through a deep experimental analysis and characterization, including chemical compatibility tests, anti-leakage performance evaluation, structural and thermodynamic properties analysis and preliminary cycling stability study.