Flight instructor on training flight with student reported engine failure in flight. Returned to departure airport and landed uneventfully.

Narrative

Summary: During maneuvers at altitude; we lost fuel pressure to the right engine. After troubleshooting and securing the engine; we [advised ATC] and landed back safely at ZZZ.My student was completing his last MEI flight before his end of course check. Aircraft X came back early from maintenance and we made a same-day reservation to complete the flight. I arrived at the aircraft about XA:45 after the preflight was completed by my student. Before engine start; I confirmed that the aircraft documents were onboard; we had over 6 qts of oil in both engines; visually confirmed we had fuel in both tanks (gauges showed about 40-45 gallons per side). My student completed the run-up and preflight checklists with no anomalies. Holding short of the runway; I took the flight controls and we did three simulated engine failures using the mixtures on the runway with me acting as the student. After the third simulated failure; we exchanged flight controls; and the student completed a short-field takeoff with about 4;000 feet remaining. At 2;000 feet on upwind; we departed with a climbing right turn to east and later turned south towards ZZZ1.My student leveled off at 6;500MSL and completed the pre-maneuver checklist about halfway between ZZZ and ZZZ1. I let him choose the first maneuver and he chose to do a steep turn. About halfway through the first steep turn (going left); I noticed that the fuel pressure to the right engine was dropping. I let him complete the turn and I announced that I was taking flight controls. I completed a quick engine kill flow and confirmed that we had lost fuel pressure and fuel flow to the right engine. I turned us back towards ZZZ and had my student complete the engine failure checklist. He was unable to restart the engine; so I had him take flight controls and tried a few additional steps myself; namely trying crossfeed on the fuel selector. I was unable to restart the engine; so I ran the securing checklist while my student feathered the engine. While he remained on flight controls; I communicated with the ZZZ Unicom and FBO Ops that we had an engine failure and that we were returning to ZZZ. I then switched over to ZZZ Approach to [request priority handling]; I mainly did this because I was concerned about conflicts with traffic coming into ZZZ2 or ZZZ1. By this point we had descended down to about 5;500 MSL and were five miles southeast of ZZZ. We noticed traffic to the southwest on ADS-B; so I asked the student to complete a right 360 turn. After the turn; I took back flight controls and descended to do a mid-field crossover for the downwind of Runway XX. My student ran the approach and before landing checklists. One error during this time is I had used an excessive amount of rudder trim at altitude; I noticed this and asked my student to help retrim the rudder while we were crossing over the field which he did.From the midfield downwind; we completed the single-engine pattern successfully. On the base to final turn; I dropped to about 80kts and was slightly low but was able to correct. We touched down a couple of hundred feet past the thousand-foot bars. We turned to exit at [Taxiway] 1; but I was unable to complete the turn with just the left engine. I stopped short of clearing the runway; shut down the aircraft; and notified UNICOM. FBO Maintenance came out and towed us back to the maintenance hangar while my student called ZZZ ATC to inform them we were safe on the ground. At the Maintenance hangar; we did a quick fuel pressure check with Maintenance and were unable to get fuel flow or fuel pressure on the right engine.The FBO fleet maintenance investigated the issue and found that it was an abnormal failure of the electric fuel pump that cut off fuel flow to the engine. The fuel pump has been replaced and it will test flown before it is returned to service. I called ZZZ ATC and they did not require any other paperwork for the [priority handling].