A320 pilot reported loss of Green Hydraulic system fluid and a Green Hydraulics System EDP low pressure ECAM message. The flight crew elected to hold for additional time for trouble shooting; the continued the approach to make a precautionary landing at destination airport.

Narrative

Green hydraulic system failure. ECAM - hyd g rsvr lo level and hyd g eng 1 pump lo pr. Actions coordinated a hold with approach control to hold over ZZZZZ to afford us the time to troubleshoot and coordinate a plan prior to our approach into ZZZ. Executed the 'non-normal' associated with the above ECAMS. Based on the status of the multiple failures associated with loss of green hydraulic system we declared flight 54 a priority aircraft with approach control for planning purposes. Contacted ZZZ Maintenance on VHF to foster a cohesive plan and review of the potential steps we would anticipate prior to our approach into ZZZ. Highlighted items discussed were alternate gear extension and no steering capability which will result in being towed off of the Runway. After discussion with Maintenance discussed the plan with my First Officer to find a shared mental model on which approach and expectations/cautions in what to anticipate before and after landing. I then followed up with communicating with the flight attendants providing them the test and then communicating with our customers. Approach phase coordinated a minimum of a 10 mile final with ATC. Actively reviewed and recalled ECAM ACTIONS with First Officer. Anticipating executing the Alt gear ext procedure we recalled the status page on lower ECAM related to approach procedure; ECAM directs us to turn on no.#1 eng hydraulic pump. Upon doing so; all malfunctions and status items were cleared and found normal. Landed with no degradation and taxied on our own power to the terminal. Advised flight attendants to remain seated and all was ok.