This is something that a lot of membership plugins can do, e.g. MemberPress, Restrict Content Pro, or similar membership or user group plugins. Which is best for you depends on your particular setup. From what you’re describing, you only need basic membership/group functionality (without features like payments), so I’d suggest going with a basic, free plugin from the WordPress.org repository, like Groups.
You can check out different solutions by searching for “memberships” or “groups”.