Medium Transport; High Wing; 2 Turboprop Eng
Air Traffic Control Fully Certified
Air Traffic Control Time Certified In Pos 1 (yrs) 10
Training / Qualification; Communication Breakdown
ATC Issue All Types; Conflict NMAC
Flight Crew Took Evasive Action
Aircraft; Human Factors
Training on North radar; Aircraft X a VFR CN35 at 065 just maneuvering about 15miles south of the CRP airport. Aircraft Y; IFR at 060 flying southbound underneath the CN35. No traffic restriction was given to the CN35 nor was traffic issued to either aircraft. About 7 minutes later the Aircraft X wants to report a near midair and says he had to respond to a TCAS hit for traffic. There was no other traffic close to the Aircraft X so it had to be the Aircraft Y at 060 who he was referencing. Too much confidence in the trainee led me to not ensure the traffic was issued. Take action and instruct trainee to issue traffic or restriction when you see the situation.
ATC Instructor reported that while giving training; a traffic call was never issued; following that one of the two aircraft reported a near miss.