A321 Captain reported a Trailing Edge Flap control failure on approach. Flight crew continued to landing at destination airport.

Narrative

On approach to ZZZ. We were slowing and going direct ZZZZZ at about 90 intercept to final XXR. Flaps one and we got a master caution. Followed the ECAM and recycled the flap lever. Unsuccessful. I decided to remain flying pilot and have the First Officer (FO) run ECAM and follow up. Right at ZZZZZ now I [requested priority handling] pulled heading so as not to join the final XXR. Tower complied and asked to maintain present heading. Tower offered XXC which I accepted. We were vectored north outside ZZZZZ1. Cleared for the visual; followed the ILS approach to touch down. I decided not to transfer controls to the FO as he was still under probation and just hit his one year anniversary. Also I felt I could use him more effectively reading and doing methodically. I also didn't message Dispatcher until I got to the Gate and called him on the phone. We were within 30 NM of ZZZ from when we got the first master caution and I ran out of time as I also had the FO look over his and my work. It took me a little longer than I had anticipated to get comfortable with the feel of the side stick and how much nose down pitch attitude it would have. Gusty cross winds but landing was successful and exited at Taxiway 1 a little over X000 ft. of Runway used. Calmed passengers and Flight Attendants down. Communication was normal and had an escort to the Gate.