How can I make a branch private to a certain collaborator of my project?

Question

We have been working with clients on different projects. We internally maintain our codebase at GitHub. Whenever we need to share the code, we simply add the client as a collaborator to our project and they get access to all the codebase.

Now, this can be tricky at times when we work on a milestone basis. If we add the client as a collaborator at the middle of the project in some milestone, they will get access to all the code even before the next milestone is completed.

Preferred flow for me would be I work on a dev branch and give the client the access to only the master branch. In that way whenever I want to share the code to the client (mostly at the end of the milestone), I will just check out the code to master and they will get the access.

Is it possible with GitHub? I know that GitHub has something called branch protection rules, but that doesn't let me do this.