B737 First Officer reported an engine rolled back at approximately FL210 during climb out. The pilots returned to the departure airport where the first approach was unsuccessful requiring a go around and finally resulting in a second successful approach.

Narrative

Climbing out of ZZZ at approximately FL210 noticed number one rolling back followed by the engine failure message on the digital gauge. All the associated malfunctions with a loss of the number one engine occurred. The Captain started to manually fly the aircraft and I proceeded to get vectors back to the field. The Captain eventually got the autopilot back on and handed me the aircraft and they proceeded to run the engine failure checklist and the one engine inoperative landing checklist. They contacted Dispatch and communicated with the Flight Attendants and notified the passengers. We briefed up the approach and proceeded on a vector to XXR. During a flight director anomaly we overshot the course slightly and had not begun our descent (waiting to be established) and opted to go-around since we were high. We wanted the most stable approach as possible. Flew around the radar pattern and landed without any issues. Taxied clear and the Captain had them check our brakes before we taxied to the gate. The rest was uneventful.