A319 Captain reported loss of a hydraulic system during cruise resulted in loss of spoilers; autopilot and a thrust reverser. Flight continued to destination and landed.

Narrative

Flt ABC ZZZ-ZZZ1 scheduled for XA00 departed on time. Push; Taxi; takeoff were normal. On climb out approaching level off we received a 'Hyd Y Sys LO PR' ECAM indication. Follow on ECAM actions did confirm yellow system indicator at zero. After following ECAM directions the PTU & yellow system were both turned off; and confirmed aircraft now in ALTERNATE LAW. As expected spoilers 2/4 were lost; AUTO PILOT inop; and down to a single thrust reverser. [Priority handling was requested] with ATC; PF/PM duties were assigned (FO now flying); and the decision was made to continue to ZZZ1 off the nose at the ETP (Equal Time Point). After completing all ECAM actions; QRH follow ups; and coordination with passengers; FA's; dispatch; and ATC; preparations were made to set up an extended final to ZZZ1 XXR. IAW (In Accordance With) procedures a config 3 approach with a Vref +10 approach speed was established early to account for a Direct Law flight controlled final after lowering the gear. Final and touch down were uneventful. Aircraft was met by ARFF (Airport Rescue and Firefighting); given the all clear; and subsequently shut down for a tow back to the gate. FO performed at a commendable level throughout the procedure. Additionally; all 3 Flight attendants handled the situation with professionalism and efficiency showcasing their years of experience. Cause: Unforeseen hydraulic failure is the causal factor in Aircraft X's [request for priority handling]. Prioritizing the fix strategy to properly delegate; communicate; and ensure ECAM/checklist compliance resulted in a positive end result.