Currently, the time flexibility of energy conversion systems is an issue of great operational importance considering the high integration of time-irregular renewable energy sources (e.g., solar, wind) which put an additional pressure on the conventional fossil-based systems. In addition, the reduction of fossil CO2 emissions from various energy-intensive industrial sectors needs to be addressed considering the issues of global warming and climate change. This paper evaluates the innovative Calcium Looping (CaL) cycle both as an energy-efficient post-combustion CO2 capture option and as a time-flexible thermo-chemical energy storage system. As illustrative energy conversion system to which the calcium looping cycle will be applied, a natural gas-based combined cycle power plant was considered. The net power output was about 400 - 500 MW with a 90 % CO2 capture rate. Corresponded non-decarbonized case was also considered to calculate the CO2 capture penalty. In-depth modelling, simulation and thermal integration evaluations were done to cover the following relevant operational elements: characterization of decarbonized combined cycle power plants with CaL cycle with / without solid sorbent storage; mass and energy integration issues; detailed techno-economic and environmental calculations of main performance indicators; flexible part load operation of the power plant to take advantages of CaL thermo-chemical energy storage characteristics etc. As the results show, the flexible time-operation of the decarbonized power plant integrated with CaL cycle using sorbent storage option improves the overall performances e.g., capital cost reduction up to 10 %, lower electricity production cost up to 5 % etc.