A320 Captain reported an NMAC event during initial approach. The flight crew complied with the TCAS RA until clear of conflict and proceeded normally.

Narrative

On our flight from ZZZ to ZZZ1; we were descending on the ZZZZZ arrival and had just crossed ZZZZZ1 at 7000 ft. We continued to descend through 6900 ft. when we received a traffic call from ATC. The Controller indicated that the traffic was at 10 o'clock at around 5500 ft. and climbing. They told us to level off immediately. They spoke quickly so I was not sure what they said. I asked for confirmation that they wanted us to level off. They confirmed and we then received a TA. The First Officer (FO) Pilot flying (PF) leveled off and announced 'TCAS I have control'. We immediately received an RA with the RA order 'Monitor Vertical Speed'. We followed the procedure for an RA; both announcing 'Autopilot off; flight directors off.' The FO disengaged the autopilot and I turned off the flight directors. My Navigation Display (ND) displayed a red traffic symbol at -3 at almost the same location as our Own Ship symbol. I looked out my window and saw the traffic; a high wing prop aircraft; passing below us at about 300 ft. below our altitude. At this point we were at approximately 6300 ft. After a few seconds we received a 'Clear of Traffic' call from the TCAS system. I told the Controller that we had received an RA. They told us that the traffic was not a factor and cleared us directly to ZZZZZ2 to cross at 4100 ft. and were cleared for the ILS XX approach. The rest of the flight proceeded normally.