I am pretty sure you can add it on TA by going to the review section, click the arrow down portion, and then a piece comes down with an add a listing option. You fill in all the details and follow the prompts to the end. At that point, I think, Trip Advisor contacts the business for acceptance or approval. Then it appears for others to see.
I went through this procedure in early March of 2016. It took a little time for it to appear but the business finally showed up on TA.
Good Luck NancyS2008
Ken is correct; you can submit a review for a new place and then TA will research to make sure it is a legit business before they add your review to the website. There is no way to call TA on the phone to add the business. The review has to be genuine and not promotional.Edited: 09 June 2016, 10:46
I don't believe you need to actually write the review at the time you submit the request to add the restaurant (at least in the past this was the case). If you do write the review at the same time as you make the request, it's a good idea to copy and paste your review into a Word document (or similar). That way, if there's a problem with the request, you'll still have your review and can submit it later, after the problem is resolved (in other words, don't count on TA to save your review).