How can I contribute to a contrib module within the context of another active site?

I am working on a new feature for a contrib module. I have created an issue and followed the new process just put in place for contributing code, as described on Creating issue forks and merge requests.

I would like to contribute to that module within the context of the site that is driving this new feature, but I am unsure of how to achieve it and still be able to test the changes introduced in the issue fork.

How can I achieve it?