With the development of Chinese society, there is an increasing demand for emissions reduction and the stable operation of the power grid. Regional comprehensive energy supply systems have entered the public’s view owing to their advantages of reducing capacity, unified dispatch, improving efficiency, and reducing energy consumption. This paper focuses on a system under construction in Chongqing, which adopts a combined gas tri-supply (combined cooling, heat, and power, CCHP) and dynamic ice storage cooling system as the research object. By establishing a mathematical model for the simulation research, this study examines the start–stop priority sequence of the gas tri-supply subsystem and the heat pump subsystem under the ice storage priority strategy in winter and summer and proposes corresponding optimization solutions. By comparing the annual operating energy consumption of the system, we conclude that the gas tri-supply composite system has good economic efficiency and peak-shaving capability, indicating that regional gas tri-supply composite systems have great application potential in the future. The proposed optimized operation strategy and simulated energy consumption calculation provide theoretical guidance for the construction and operation of both this project and similar projects.