Narrative:

We were a training flight leaving ZZZ after a practice ILS on a 180 heading. We were still monitoring ZZZ tower; but were not in direct contact with them. Climbing through 3;500 feet I noticed an aircraft 500 feet above us approximately 10 miles to the east of our position on a converging path. I assumed the aircraft was a slow moving aircraft. We usually don't see jets this low around this area. As we were reaching 4;000 feet; I double checked TCAS and noticed the traffic I previously saw was rapidly closing distance. I spotted the aircraft at my 10 o'clock; which was on a course to collide with us. I made a 60 to 70 degree bank turn to the right and began a rapid descent; while keeping the traffic in sight. Nothing else came out of the situation. I called ATC approach after landing at ZZZ1 and talked to one of the controllers who was on duty when the incident happened. He informed us that if we hadn't taken action; the situation could have ended with a grim outcome. He gave me some tips of how they handle their inbound aircraft in that area; and I will pass those tips onto the rest of my company.

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Original NASA ASRS Text

Title: DA-40 flight instructor and instrument pilot in training reported a NMAC.

Narrative: We were a training flight leaving ZZZ after a practice ILS on a 180 heading. We were still monitoring ZZZ Tower; but were not in direct contact with them. Climbing through 3;500 feet I noticed an aircraft 500 feet above us approximately 10 miles to the east of our position on a converging path. I assumed the aircraft was a slow moving aircraft. We usually don't see jets this low around this area. As we were reaching 4;000 feet; I double checked TCAS and noticed the traffic I previously saw was rapidly closing distance. I spotted the aircraft at my 10 o'clock; which was on a course to collide with us. I made a 60 to 70 degree bank turn to the right and began a rapid descent; while keeping the traffic in sight. Nothing else came out of the situation. I called ATC approach after landing at ZZZ1 and talked to one of the controllers who was on duty when the incident happened. He informed us that if we hadn't taken action; the situation could have ended with a grim outcome. He gave me some tips of how they handle their inbound aircraft in that area; and I will pass those tips onto the rest of my company.

Data retrieved from NASA's ASRS site and automatically converted to unabbreviated mixed upper/lowercase text. This report is for informational purposes with no guarantee of accuracy. See NASA's ASRS site for official report.