A321 Pilot reported loss of airspeed indications on both the Captain's and first Officer's PFDs. The flight crew performed an air turn back and precautionary landing at departure airport.

Narrative

During takeoff roll; lost CA (Captain) and FO (First Officer) airspeed indications. Standby airspeed indicated properly. Once airborne; ECAM (Electronic Centralized Aircraft Monitor) messages indicated that the aircraft was in alternate law and had no autopilot or auto thrust. CA and FO had no flight directors. Upon flap retraction; flaps jammed (leading edge slats failed to retract). ECAM displayed use manual pitch trim. Unable to manually trim aircraft pitch. Aircraft was nose-heavy. Required continuous aft stick pressure to maintain level flight. Believe maximum flap/slat speed exceeded. [Requested priority handling]. Returned to ZZZ. Able to configure aircraft to flaps 3. Upon gear extension; regained normal pitch authority. Uneventful landing and rollout. After clearing the runway; flaps retracted normally. Aircraft logbook indicated that the #3 pitot tube had been replaced due to being clogged. The logbook also indicated the aircraft had a hard landing on the previous flight. Multiple system failures. I do not know the cause of the system failures and therefore do not have any suggestions on how to prevent this from happening again. Previous simulator training with simulated systems failures was definitely helpful in this situation.