Featured with fast response abilities and high ramp rates, energy storage systems (ESS), such as pumped-storage hydropower (PSH) plants and battery storage systems (BSS), are considered as key first-responders to provide spinning reserve in response to system contingencies. However, ESSs are energy-limited resources, and their sustained spinning reserve deployment is restricted by the stored energy and available capacity. Indeed, the spinning reserve deployment against contingencies may deviate actual state-of-charge (SOC) from the scheduled value, inducing potential SOC boundary violations and non-dispatchability in later hours. This paper proposes the post-contingency operation model and the spinning reserve secure constraints to address these issues. The post-contingency operation model describes that spinning reserve from ESSs is promptly deployed when contingency occurs, and then gradually substituted by quick-start units when they are switched online. By leveraging this operation strategy, spinning reserve secure constraints in terms of SOC headrooms are adopted to guarantee its deplorability. A modified IEEE 118-bus system with multiple PSHs and BSSs is used to verify the proposed approach.