Have you looked at category permissions? If you go to a category page, click “edit” and then the “security” tab you can set permissions for what user groups can see, reply, and/or create topics in that category.
In this case, sounds like removing the default permissions setting (everyone) and adding a rule so trust_level_0 users can create / reply / see the category might do the trick. You could also e.g. make it so tl0 (all users) can see, but only tl1 users can create / reply, or something like that.