Integration of Distributed Energy Resources (DERs) can introduce challenges such as Over-Voltage (OV) and line congestion in distribution networks. Recently, the concept of dynamic export limits as well as Community Energy Storage (CES) have gained attention as potential solutions for these challenges. Within these concepts, this paper presents a novel framework where the Distribution Network Service Provider (DNSP) provides prosumers with dynamic export limits for networks with a CES. Moreover, this framework enables prosumers (through leasing) and the DNSP to collaboratively manage the CES. In each time step, the DNSP calculates the charging/discharging power for the unleased portion of the CES and collects data on the expected export and charging/discharging power from prosumers leasing the CES. Subsequently, while considering network voltage and current limits and a fairness objective, the DNSP computes and communicates dynamic export limits to prosumers, allowing them to manage their assets accordingly. The performance of the proposed framework is evaluated via various case studies conducted on a real-world LV test feeder with 49 prosumers. The results emphasize the critical role of dynamic export limits in resolving OV and congestion issues in DER-rich networks. Furthermore, the CES proves to be effective in reducing active power curtailment and increasing total generation, with a notable increase of 4.6%.