The scientific aim of this work is to encourage energy conservation. This article offers a fresh perspective on renewable energy in the air conditioning sector, the country’s economic growth, and environment-friendly techniques to overcome global warming challenges. In this research, a solar vapor absorption refrigeration (SVAR) system was combined with a conventional vapor compression refrigeration (VCR) system to analyze their combined performance, employing a compound parabolic collector (CPC). The goal was to assess the performance of a solar hybrid cooling system using this non-tracking solar collector. CPC was validated for heat output with 2.9% uncertainty by utilizing an engineering equation solver (EES). Other system components were also validated with EES and then extended to a larger-capacity solar hybrid cooling system. The results of this research indicate that CPC is effective in providing the required heat to SVAR throughout the year without any tracking, and the integration of SVAR in series with the VCR condenser produces 83% higher COP than the system that integrates VCR with the condenser of the SVAR system for Riyadh. The configuration results in high values of exergy COP and an efficiency of 88% and 84%, respectively, increases the cooling capacity of the VCR by 68%, and decreases the carbon emission by 166.4%.