In broad terms you’re going to:
- Create a group via /groups
- Create the new category and delete the ‘everyone’ permission, replacing it with the group which will have access and the appropriate permission. If your users will be allowed to create topics they will need ‘create/reply/see’, whereas if they’re only going to be allowed to respond to existing topics you can go with ‘reply/see’.
It will only be visible to those within the group, with a padlock next to the category name to indicate that it’s secured from general users.
Users can either be added to the group manually, or you can add the Access option “Allow users to send membership requests to group owners” which will let them apply, and the owner(s) approve as necessary.