We have contracts with regulated companies (health care). The contracts require us as a vendor to monitor and comply with laws that cover our work with our clients. Our client health care companies also have the right to review our performance and processes.
I'm not sure how to perform or track compliance reviews related to a contract.
Within your contract management system, create a form that lets you pick the compliance requirement. The form should allow you to summary the purpose of the review. It should also give you space to indicate the outcome of the review. Ideally, you could keep a history of each update.