You would need to cut the wires with plug from the tire mount that you took off and splice it onto the wires on the new licens plate frame. Make sure to cut enough of the wires from the tire mount. If you don't want to cut the wires, you can probably get a new harness from the dealer.
Sorry reread your post...Look under the rear bumper, passenger side. There should be a plug there that was hooked up to the light on the tire mount. You can splice onto there.