SR20
Flight Crew Flight Instructor; Flight Crew Instrument; Flight Crew Multiengine
Flight Crew Last 90 Days 20; Flight Crew Total 7000; Flight Crew Type 1000
Conflict NMAC
Air Traffic Control Issued Advisory / Alert; Flight Crew Took Evasive Action
Aircraft; Environment - Non Weather Related; Procedure; Human Factors
I was conducting an initial Part 141 check for a flight instructor. We requested a Northbound departure and were assigned Runway XXR. Once on a northbound heading we were given a traffic alert from ZZZ Tower for traffic at our 1 o'clock position. We lowered the nose slightly to gain visual.  The traffic passed below us on a Westerly heading. ZZZ Tower informed us the aircraft was with ZZZ1 Approach executing a missed approach from Runway XXR. [The difference in our altitude] was 2;700 ft. MSL [for our flight] and the other aircraft was 2;500 ft. MSL.
Pilot reported that ATC issued a traffic alert while on departure resulting in a NMAC.