A321
Flight Crew Multiengine; Flight Crew Instrument; Flight Crew Air Transport Pilot (ATP)
Communication Breakdown
ATC Issue All Types; Conflict NMAC
Flight Crew Took Evasive Action
Human Factors; Procedure
After takeoff we delayed our Tower assigned turn to 120 until reaching1;000 ft. per the company Ops pages. We received a RA (TCAS resolution advisory) at about 1;000-1200 ft. We responded to the RA. Informed the Tower immediately; they did not acknowledge our report and switched us to Departure. After we were cleared of the conflict we noticed an aircraft on the MFD 400 ft. above us. The Tower Controller cleared us for take off with a turn to 120 before we reached the runway; suspect the departure corridor was not clear. Better communication between flight crew and ATC; about traffic awareness in the vicinity of the airport.
Departed RWY XXR ZZZ; per company pages started right turn to heading 120 assigned by ATC. Immediately received an RA 'monitor vertical speed' we were climbing at about 1500'/min and v/s (Vertical Speed) tape showed we needed to limit climb to about 200'/min. We pitched over immediately; shortly thereafter we got 'clear of conflict'. All this happened between about 1;500 feet AGL and 3;000 feet. After the RA was complete I noticed traffic on the ND (Navigation Display) about 400 feet above us and slightly behind us. During the event Tower handed us off to Departure; we told him we were responding to an RA. Without any comment he repeated the hand-off to Departure.We were following our assigned clearance.  We do not know who the other aircraft was or if they had deviated from their clearance. It all happened very fast at a busy phase of flight. Pull the [Quality Assurance] data for this flight and ATC records to see what caused this event. I believe we got close to this other aircraft but I don't know why. I think it's worth investigating.
Air Carrier Captain Flying A321 aircraft reported NMAC after takeoff.