http://www.shelbycountytn.gov/index.aspx?NID=585

From DMV.org

Utility Trailers
Tennessee doesn't require you to title or register your utility trailer unless you plan to take it to another state.

If that's the case, you'll need to take the original title (if you have one), your driver's license, and the $10.50 fee to your local County Clerk's office.