A319 flight crew reported a pressurization issue during descent. Flight crew requested a lower altitude from ATC and continued to an uneventful landing.

Narrative

During descent from FL 260 to FL 220 and direct to ZZZZZ on the ZZZZZ1 arrival into ZZZ. We were set up for a hold at ZZZZZ due to weather in ZZZ. I noticed the cabin press status page was displayed and the cabin alt flashing with a 5-600 FPM climb on the cabin VSI. Cabin alt was at 9000 and climbing. I alerted the (FO) First Officer to this and we agreed it was not normal. We immediately divided roles into flying/non flying pilot to have a clear understanding of how we would handle this. I instructed the FO to bring up the non normal excs cabin alt to have it ready in the FM (Flight Manual). He informed ATC that we had a pressurization issue and would need an immediate descent. ATC vectored us off our routing to the hold and descended us to FL180 for traffic. Cabin alt was now at 12000 and still climbing with the VENT; EXTRACT; OUTFLOW and SAFETY VALVE displaying yellow on the status page. The cabin alt was flashing red. After clearing traffic below; we initiated a descent to 10000 ft. Once leveling at 10000 we got a excessive lo cabin diff pressure ECAM. We ran the ECAM and corrected the PSID. We then descended to 9000 to avoid use of O2 masks and get the cabin to a safe alt. An emergency was not declared as we were able to remedy the cabin alt with the descent but emergency authority was used to get priority handling out of the holding stack and down to 10000. If we did not get the decent; we both believed that the pax oxygen masks would have deployed and we would have been required to use crew O2 due to high cabin alt. We used CRM to fix this situation and avoid an impending excess cabin alt ECAM. The FO did an amazing job handling the workload from not only a possible diversion due to the weather before hand but also the non normal of a rapidly climbing cabin alt. A write up and debrief was conducted at the gate after an uneventful landing on Runway XXR.Eng anti ice was ON FL260-FL150