Flight Instructor reported no engine response to throttle movement and returned to land immediately at departure airport.

Narrative

During student pilot training flight engine throttle was brought to idle for engine out training procedures. Engine indication showed an unusually high RPM for the idle position. Instructor took control of aircraft to troubled shoot and run checklists. Instructor contacted ZZZ Approach to [Inform] an issue may be occurring and requested monitoring during return to ZZZ. ATC asked if [requesting priority handling]. At the time Instructor said to standby to take time to trouble shoot and evaluate. Instructor still provided ATC with all needed information. When Instructor unable to clear the abnormal reading and aircraft RPM did not appear to slow [requested priority]. On final approach to land shut down engine as the RPM would still not go to idle. Engine was then secured and aircraft safely landed on runway. No injury or aircraft damage occurred. Aircraft grounded and moved to maintenance for engine inspection. Instructor requested re-training event with Safety Officer and Chief Pilot to evaluate situation and makes sure Instructor is safe and knowledge before return to flight line.