PA-28 Flight Instructor reported that during a training flight the engine fuel pump failed. Flight returned to the departure airport.

Narrative

Student and I were taking the aircraft up to become familiar with it. Student (part Owner; Student Pilot) had just taken possession the day before and was unfamiliar with Pipers. Ferry Pilot had brought the aircraft up from California; reported no major mechanical issues; none were observed during preflight. Fueled the aircraft full prior to departure from ZZZ; unrestricted VMC day; normal flight; no indications of problems. I decided to stay near the airport (5-10 miles) in case of problems; Student concurred. We did some maneuvers; slow flight; steep turns; stalls to get a feel for the airplane. Came back and did some more steep turns. During the middle of the maneuver; Student noticed the fuel warning light come on and announced it to me. I checked the Fuel Pressure Gauge; it was low and dropping. He asked if we should turn on the electric pump; I said yes; and it restored fuel pressure. All tanks were over 75% full; had been in the air less than 2 hours. We discontinued the flight at this point and made an immediate return to base to ZZZ (nearest airport). Elected to stay at altitude (approximately 5000 ft. MSL) till within gliding distance of the airport. Uneventful landing; suspected engine driven fuel pump failure.