Flight Crew Commercial; Flight Crew Flight Instructor; Flight Crew Instrument; Flight Crew Multiengine
Flight Crew Last 90 Days 250; Flight Crew Total 4000; Flight Crew Type 4000
Situational Awareness; Communication Breakdown
ATC Issue All Types; Conflict NMAC
Flight Crew Took Evasive Action
Procedure; Airspace Structure
During a routine training flight in the traffic pattern at ZZZ; I was flying with a student in the traffic pattern. I had just turned downwind when Tower called out to make a sudden left turn. When I did so I saw a Learjet that had just turned crosswind from Runway X in my line of sight. I pulled power back and pushed the nose down. The Learjet was in a hard climb and we missed each other with no problem. It was unnerving and if either myself or the Learjet pilot had erred in evasive action; there was a very real possibility of a midair collision.
We were cleared for takeoff Runway X by ZZZ Tower and assigned a heading of 340. After takeoff and passing 700 feet AGL; we were established on the 340 heading. TCAS alerted us to a possible conflict at 12 o'clock. We increased climb rate and passed above the conflicting traffic that appeared to be on downwind for Runway X. No TCAS RA was received.
PA28 and LR75 flight crews reported ATC error resulted in an NMAC.