As an achievement of innovations resulting from partitioning mechanisms, these mechanisms can contribute to the more flexible operation of power systems in local communities. The ever-increasing frequency and severity of unexpected real-time failures have created challenges for partitioned-based power system operators, affecting each partition's resiliency. With this in mind, this paper presents an adaptive local operation strategy (ALOS) for resilient scheduling of the renewable-dominated partitioned-based power systems under normal and islanding modes in a decentralized manner. The main objective of the developed ALOS lies in reaching an affordable preparedness level in each partition to deal with unscheduled islanding mode, which can occur subsequent to real-time failures at common lines between adjacent partitions on transmission level. To this end, a set of resilience-target constraints is presented to prepare sufficient spinning reserve capacity in each partition to ensure continuity of supply during islanding mode. The proposed strategy is formulated as a two-stage stochastic mixed-integer linear program (MILP), and the nested formation algorithm is employed to execute it in a hierarchical fashion based on the privacy-preserving protocols. Besides, the tri-state compressed air energy storage (CAES) system is also included in the proposed strategy to mitigate the negative consequences caused by real-time failures and uncertain sources. Numerical results conducted on the IEEE 30-bus test system reveal that the proposed ALOS can enhance the resilience of each partition in responding to unscheduled islanding mode by efficiently utilizing all available capacities on the generation side. Furthermore, the DIgSILENT PowerFactory is used to identify the worst possible series of events and to evaluate the effectiveness of the proposed resilience-promoting proactive strategy in dealing with these events.