The development of Terahertz (THz) detectors suitable for biological and cellular systems remains a significant challenge due to limitations in detector miniaturisation and operating principles. Solid-state point defects, with their unique optical and microwave responses, offer promising avenues for advancing THz detection technologies. Among these, rare earth ion doped crystals stand out due to their unique properties. While spectroscopic investigations of these materials have primarily concentrated on the visible, infrared, microwave, and radio frequency bands, studies in the THz range remain notably underexplored. In this study, we explored the crystal properties of cerium-doped yttrium aluminium garnet (Ce:YAG), focusing on the splitting of its ground-state energy levels. Crystal field splitting of the 4f level resulted in seven distinct peaks, with energy differences calculated at 8.45, 4.10, 23.5, 4.10, 15.1, and 46.8 THz. Our simulations demonstrated that the incorporation of cerium ions induces ground-state splitting at THz frequencies, suggesting that this doped structure holds potential for THz wave response and the development of a novel THz sensor.