Instructor Pilot reported engine RPM loss after take off. The flight crew immediately turned back to the airport and requested priority handling. The Instructor Pilot landed and taxied back to the ramp; followed by Airport Ops and ARFF vehicles.

Narrative

After a totally normal preflight and run up; a student and I began doing touch and gos at ZZZ. We had 7 totally normal landings and takeoffs with no issues. On departure for our 8 lap in the pattern the student and I noticed 200-300 RPM loss at approximately 800 feet AGL. I took controls immediately; made a 180 degree turn back to the runway. Informed Tower of RPM loss and requested immediate access to all runways requesting priority landing. During the turn I increased mixture to full rich and adjusted throttle but continued to have RPM drop then raise uncontrollably and unpredictably which was noticeable by the sound and thrust created by the engine. Tower cleared me for all runways; I ensured I had adequate altitude and airspeed to make the runway then added flaps to 20 degrees and entered a forward slip down to the runway. We landed safely with zero injuries or damage. Airport Operations and Fire Crew followed me during my taxi to parking and concluded there were no fluid leaks. I gave a verbal report to Airport Operations volunteering all information. I spoke to Company Superiors and ensured the airplane was taken off the line and would not be flown until inspected by Maintenance.