Ensuring the secure and proper deployment of Enclaves is critical for the security of Trusted Execution Environments (TEEs). Recently, the increasing attacks targeting Enclaves have made the traditional solution risky to use different enclaves for each task. An ideal solution is a pre-designed enclave that can be flexibly reused across different computational tasks. To address this issue, we propose FH-TEE, a novel framework that integrates Fully Homomorphic Encryption (FHE) with TEE. In this approach, computational tasks are partitioned so that only fixed, logic-independent operations are performed within the Enclave, enabling its reuse across various tasks. Flexibility in accommodating diverse computational requirements is achieved through FHE. Furthermore, because computationally intensive FHE operations, such as bootstrapping and ciphertext transformation, are logic-independent and offloaded to the Enclave, FH-TEE significantly improves efficiency compared to purely FHE-based solutions, while maintaining robust privacy and security. In our demo program, the server receives ciphertext from the client, performs ten iterations of the Game of Life computation, and then sends the resulting ciphertext back to the client. The results show that our scheme is \(10.57\times \) faster in computation speed and \(32064\times \) smaller in transmission size compared to a pure FHE scheme.