Distributed ledger technology (DLT) is well-suited for decentralized environments and can improve collaboration and coordination among multiple stakeholders. There are many DLT systems offering a variety of decentralized services, powered by different or similar DLT solutions. However, these DLT systems are often isolated from one another, making it valuable to connect them through cross-chain services. The cross-chain services enable data and transactions to move between different DLT systems and allow them to interact seamlessly. Since these services jointly handle user data and transactions in decentralized environment, they face significant security and privacy risks. Therefore, it is essential to study and establish security requirements and a robust framework to strength security of cross-chain service for DLT systems. This Recommendation introduces the concept of cross-chain service to achieve interoperability of DLT systems. It also specifies security risks, requirements, framework and capabilities, as well as general procedures to ensure security of cross-chain services for DLT systems interoperability.