Small Transport; Low Wing; 2 Turbojet Eng
Flight Crew Air Transport Pilot (ATP); Flight Crew Instrument; Flight Crew Multiengine
Flight Crew Last 90 Days 225; Flight Crew Total 5070; Flight Crew Type 2530
Communication Breakdown; Distraction; Time Pressure; Troubleshooting; Workload
Conflict NMAC; Deviation - Altitude Crossing Restriction Not Met; Deviation - Altitude Overshoot; Deviation / Discrepancy - Procedural Published Material / Policy; Deviation / Discrepancy - Procedural Clearance
Flight Crew Took Evasive Action
Human Factors; Environment - Non Weather Related
Departing Runway XX from ZZZ. Issued climb via SID to 20;000 ft. Briefed approach with crew. In the turn near ZZZZZ became aware of visual target approaching left to right. ATC was asking target about altitude which led crew to believe he wasn't where he was expected to be. Target was now 300 ft. above and appeared to have until now been in a descent. Traffic alert sounded in cockpit. Quick review of terrain on departure plate showed rising terrain 13;000 ft. and TAWS showed red to the left. Unable to transmit to ATC due to conversation between target and ATC. Elected to climb to avoid terrain and target. Disconnected autopilot for climb and preparation for potential evasive action. Climbed above published 'at or below' crossing restriction. Believe we were within 3 miles of crossing when we topped the altitude. Crossing restriction missed by crew due to distraction with traffic alert and eyes outside for see and avoid operations. Upon review after the fact; target on arrival should have been at 10;000 ft. and our level off at 9;000 ft. would have kept us below target. We did not have that information at the time of the incident which is why we believed the target was descending and our climb would have avoided the conflict.
Captain reported taking evasive action to avoid a NMAC while on a SID resulting in a missed crossing restriction.