Captain reported loss of the Green Hydraulic System in cruise. The flight crew continued to destination airport and landed.

Narrative

Flight from ZZZ started out pretty normal; earlier in cruise flight we had an ELAC2 computer reset. The event happen around XA59z in cruise. The ECAM reported a (HYD G RSVR LO LVL / HYD G ENG 1 PUMP LO PR / HYD G SYS LO PR). We ran the ECAM action and the COM2; and recognized that we would have to lower the landing gear via a gravity extension. At this point I knew we had commuter that was headed to ZZZ1. Since I was doing IOE with the First Officer; I thought it would be better to have more input on the situation especially from an Instructor. I notified the Flight Attendants; the Company and [requested priority handling] and continued to ZZZ1. I requested a longer then normal approach to final for the flight control and the gravity gear extension. Landed the airplane on Runway XXR from the ILS; came to a complete stop on the Runway ran the emergency procedures with fire and rescue. I taxied to the Gate with no incident after land and park checklist completed. I reserve the right to amend this report as additional information becomes available to me.