A320 pilot reported av HYD G ENG 1 PUMP LO PR ECAM in flight. This was followed by a HYD G SYS LO PR. The flight crew elected to continue the flight and make a precautionary landing at destination airport.

Narrative

Climbing out of ZZZ at approximately 13-14;000 ft.; we experienced a HYD G ENG 1 PUMP LO PR ECAM. Name ran the QRC then we divided our duties. As I started to run the LO PR ECAM it disappeared. I went to the HYD page and saw the G HYD fluid was low. Less than a minute later we received the HYD G SYS LO PR. I ran the ECAM; accomplished the QRH and contacted Dispatch and Maintenance. I discussed the issue with Maintenance and from their end he could see the the HYD G SYS LO PR. We agreed all the procedures were accomplished and discussed whether to continue or return to ZZZ. Maintenance stated that nowhere in the ECAM does it say land ASAP and it would be safe to continue on. Dispatch agreed the weather in ZZZ1 would be fine at arrival and I also agreed it was safe to continue. Name and I talked about what we need to do as we got closer to our destination. We ACARS'd dispatch that we would need to be tugged off the Runway for lack of NWS. The decision was also made that we would [request priority handling] with ZZZ Center so ZZZ1 can prepare for our arrival. We discussed when we would extend the gear and talked about the other Inop Sys associated with the G Hyd. I called the Flight Attendant 1 to the cockpit to explain the issue and what to expect. I gave her the alert and she was to tell the other inflight of the issue and to contact me with any questions. We requested priority handling with ZZZ Center. In the descent we informed the customers that we would be stopping on the Runway to remain seated till we were at the Gate. The ZZZZZ arrival was uneventful and we were given Runway XXL. We requested a long final to manually extend our gear and finish our remaining checklists. The landing was uneventful We stopped on the Runway and crash fire rescue met us at the plane. We were talking to our tug in minutes; engines were shut down and we were tugged to the Gate. Maintenance meet us at the plane and they were given a debrief.