In response to the growing demand for sustainable and efficient energy management, this paper introduces an innovative approach aimed at enhancing grid-connected multi-microgrid systems. The study proposes a strategy that involves the leasing of shared energy storage (SES) to establish a collaborative micro-grid coalition (MGCO), enabling active participation in the dispatching operations of active distribution networks (ADNs). A hierarchical framework wherein the ADN assumes the role of the central orchestrator is developed, while the MGCO and SES operators (SESO) function as responsive entities within a single-leader multi-follower game optimization model. The ADN leader implements timeof-use (TOU) pricing mechanisms as a strategic incentive to encourage active engagement from the MGCO and SESO followers in peak regulation dispatch activities. In response to these TOU policies, the followers implement a two-stage dispatch optimization strategy. The first stage is dedicated to optimizing energy storage utilization. Within this phase, each microgrid meticulously fine-tunes its energy storage charging and discharging strategies with the primary objectives of mitigating power fluctuations, reducing load variance, minimizing energy storage costs, and facilitating on-demand leasing of energy storage resources. Subsequently, energy storage resources are pooled and shared to harness collective benefits and enhance alliance-wide energy utilization. Emphasis is placed on prioritizing the integration of renewable energy sources, promptly responding to peak demand regulation and scheduling, maximizing overall benefits, and equitably distributing cooperative advantages among alliance members. To substantiate the effectiveness of this comprehensive methodology, the paper presents illustrative results that provide compelling evidence of its potential to facilitate the seamless integration of microgrids, shared energy storage, and active distribution networks.