In this work, first-principles calculations based on density functional theory (DFT) inside the Quantum ESPRESSO framework are used to investigate the structural and electrical properties of vanadium carbide (VC) and vanadium nitride (VN). Hybrid exchange-correlation functional, specifically the PBE0 hybrid functional, and a modified potential model incorporating covalency effects are employed to enhance the accuracy of the predictions. The study explores structural phase transitions, volume collapse, and other ground-state properties by comparing the results of the conventional GGA-PBE approach with theoretical and experimental data. The electronic possessions, including band structures and densities of states (DOS), are analyzed for both the parent and high-pressure transition phases, providing crucial insights into the electronic structure, phase-dependent conductivity, and metallization effects. The findings contribute to a deeper understanding of transition metal carbides and nitrides under extreme conditions, with potential implications for high-pressure physics and advanced material applications.