A320 Captain reported a loss of a hydraulic system during cruise. The flight continued to the destination and landed but required a tow from the taxiway to the gate.

Narrative

Approximately 1 hour before arrival into ZZZ; we got a ECAM .. HYD G ENG 1 PUMP LO PR..G SYS LO PR. The first officer and I ran; per SOP; ECAM actions and QRH. We realized there would be a potential for numerous systems associated with the G HYD system that may be inoperative. No Normal braking; no auto brakes... to name a few. I contacted dispatch and maintenance control. After concurring with Maintenance Control that we had done everything possible and dispatch verified the QRH procedure and calculating landing distance required with loss of braking and single reverser. We proceeded to notify the cabin crew; ATC and customers.I had the purser come into the cockpit to brief him on the situation and told him it would be a moderate level situation; which could escalate to an urgent situation. We then continued the arrival and [requested priority handling] with ZZZ approach and were given runway XXR ILS.I then made a PA to the customers advising them that we had lost one of our hydraulic systems; but to be rest assured we have 2 other systems. I did tell them out of abundance of precaution we [requested priority] and that CFAR (Crash Fire and Rescue) will meet us upon landing. I advised them them to follow all flight attendant instructions and to give them their undivided attention.We turned on the Hyd engine and PTU (Power Transfer Unit) on to put the gear down with the remaining fluid;we did this on base leg; in case it failed to come down; we could do a manual extension.Gear came down and locked. We turned the pumps back off and turned them on just before touchdown to use it for braking and steering.After landing XXR we were able to taxi off the runway; where we started the APU and shut down the engines and had the aircraft towed the remainder of the way to gate XX.