B737-800 First Officer reported an electric trim failure during climbout resulting in an immediate return to the departure airport

Narrative

During climbout I tried to use the electric trim and it did not work. I informed the Captain and handed over the controls to see if his side would respond. The Captain's side didn't respond either. We informed ATC and requested to stop our climb at 4;000 feet and get delay vectors around the ZZZ airport; while we ran the QRH and came up with our plan. After the Captain talked with the Chief Pilot on Call; we decided to make an overweight landing in ZZZ. We coordinated with the Flight Attendants; notified the Passengers and requested the fire trucks to be standing by in the event of hot brakes. We landed safely on Runway XX in ZZZ with flaps 15; and came to a stop on the taxiway to allow the Fire Department to check the brake temperatures. While the inspection was taking place; we requested the brake cooling data from the ACARS. The Fire Department determined the brakes were safe and the data supported a return to the gate under our own power. We coordinated with Operations for a gate return. We never set the brake; and Ramp Personnel chocked all of the tires.