A319 Captain reported they lost control of cabin altitude in the descent; and requested an expedited descent from ATC.

Narrative

During descent on the ZZZZZX arrival; we noticed a strong tailwind would challenge the FMGC to meet crossing restrictions. My attention was distracted by crossing; I did not see the cabin altitude issue until First Officer (FO) pointed it out; at about 24;000 feet. The cabin altitude was already at 9;500. As pilot monitoring (PM); I asked for and received an expedited clearance to 15;000 and relief from the 210 kt. speed assigned by ATC previously. It became apparent the the cabin altitude would exceed 10;000 feet about the time we passed 16;000 feet. We received an ECAM for off schedule descent I believe. We ran the ECAM; and observed the delta p was zero. The safety relief valve was open on the pressurization page. I [requested priority handling]. FO disconnected the Autopilot and auto thrust to further expedite our descent. We caught the cabin at around 11;000 feet. I contacted the purser; confirming that the passenger oxygen had not deployed. We were cleared for approach to Runway XXL. I had not pulled landing data for that runway. Uneventful approach and landing after 10;0000 feet.