Rapidly increasing global energy demands requires sustainable alternatives to conventional fossil fuels. Hydrogen emerges as a promising energy carrier due to its high energy density and minimal environmental impact, mainly when produced via thermochemical cycles like the Copper Chlorine (CuCl), which makes use of low-grade waste thermal energy for hydrogen production in an environmentally friendly manner. This study integrates hydrogen production using the Cu-Cl cycle and hydrogen compression systems crucial for establishing robust hydrogen infrastructure. Following hydrogen generation, the study examines the thermodynamic analysis of compressing hydrogen to higher pressures. Parametric variations in compression, including inlet and outlet pressures and the number of stages, are analyzed to optimize energy efficiency and exergy performance. Energy efficiency of around 47.05% is obtained for the 4-step Cu-Cl cycle. The integrated step showed a notably high exergy efficiency of 98.48%. Other key findings include a 35% increase in energy efficiency with five compression stages for an inlet pressure increment from 15 to 30 bars, and a 12% efficiency decrease when varying outlet pressure from 500 to 800 bars. Exergy efficiency shows a 17% improvement with increased compression stages under constant inlet pressure but a 4% decline when varying outlet pressure with a five-stage configuration. These findings highlight the critical role of efficient compression systems in enhancing hydrogen storage and distribution for sustainable energy applications.