It used to be that you could search for a restaurant that wasn't listed yet. It would return negative results and ask you if you wanted to request a new listing.
Unfortunately, they revamped the search page, and it now requires that the fields you put in resolve to existing listings before it will allow you to search.
I cannot find any other way to request a new listing. I tried sending an email to the help address, but it told me that I needed to go through the help center online. I tried that a few days ago and never even received a confirmation that the issue was being looked at.
This is frustrating to me because, in the past, TripAdvisor has actually been very responsive to my requests for new listings and corrections that I submitted for existing listings.