Board Thread:Support Requests - Community Management/@comment-12499468-20130717155653/@comment-3030984-20130717165448

Sorry, but Wikia don't offer private wikis.

Per Randommixer, you could give your 'trusted' users admin rights, then protect the pages you need to from editing - but you can't completely prevent other Wikia users from editing on the wiki.

However, it is very unlikely anyway that you'll have users from elsewhere editing - it sounds like a very specific topic.