Presume you have a class which passes all its current unit tests.
If you were to add or pull out some methods/introduce a new class and then use composition to incorporate the same functionality would the new class require testing?
I’m torn between whether or not you should so any advice would be great.
Edit:
Suppose I should have added I use DI (Dependency Injection) therefore should I inject the new class as well?
Not in the context of TDD, no, IMHO. The existing tests justify everything about the existence of the class. If you need to add behavior to the class, that would be the time to introduce a test.
That being said, it may make your code and tests clearer to move the tests into a class that relates to the new class you made. That depends very much on the specific case.
EDIT: After your edit, I would say that that makes a good case for moving some existing tests (or a portion of the existing tests). If the class is so decoupled that it requires injection, then it sounds like the existing tests may not be obviously covering it if they stay where they are.