I currently have a Library System UML and my question is: How do I implement a Proxy AND Adapter Pattern together?

My goal is to create a service between the UI and the services and create another model layer for the public. The service is supposed to take the model coming in and translate it to the model the inner service needs.

Here is my starting idea (My UML is bigger but I left out the unnecessary info):

- I have the RealSubject which inherits from the TitleRecord Class --> which will retrieve the Title from the Repository class (which is a Singleton Class)).

How do I add the Adapter Pattern to my Proxy? An adapter pattern should convert an interface into one the client can use so if I were to implement the adapter, would the TitleRecord be the ConcreteAdapter and the Proxy be the Adaptee? I understand the Proxy aspect more, it is the Adapter Pattern that I am having trouble with implementing. I have been stuck on this for quite some time, help is much appreciated thank you!!