C172 flight instructor reported a near midair collision during climb in VFR conditions.

Attributes
ACN	1517157
Time
Date	201802
Local Time Of Day	0601-1200
Place
Locale Reference	ZZZ.Airport
State Reference	US
Environment
Flight Conditions	VMC
Light	Daylight
Aircraft 1
Make Model Name	Skyhawk 172/Cutlass 172
Operating Under FAR Part	Part 91
Flight Phase	Initial Climb
Route In Use	Direct
Flight Plan	None
Aircraft 2
Make Model Name	PA-28 Cherokee/Archer/Dakota/Pillan/Warrior
Operating Under FAR Part	Part 91
Person 1
Function	Instructor Pilot Not Flying
Qualification	Flight Crew Commercial Flight Crew Flight Instructor Flight Crew Multiengine Flight Crew Instrument
Experience	Flight Crew Last 90 Days 50 Flight Crew Total 820 Flight Crew Type 300
Events
Anomaly	ATC Issue All Types Conflict NMAC
Miss Distance	Horizontal 300 Vertical 50

Narrative:

[Student and I] departed straight out and the tower controller gave us a cleared to turn after 6;500 feet. At about 6400 feet; tower gave us the go-ahead to turn left and we cleared the aircraft and turned left crosswind. After wings level on the crosswind the adsb warning came on and said 'traffic 9 o'clock same altitude'. I immediately looked left and saw a cherokee less than 1/4 mi on a collision course and immediately took controls and dumped the nose and power to avoid collision. I reported back to the tower that we had an aircraft fly directly over top of us with no reply other than a frequency change a moment later.I believe the cause of the problem was a very busy controller forgot to follow up with cherokee on the first call to him saying traffic 12 o'clock 6;600 feet after the pilot of the cherokee said 'looking for traffic'. This lack of communication along with cherokee doglegging his upwind leg left of runway heading on a straight out departure caused the near collision. The only thing that saved the near collision was the adsb warning in the aircraft I was flying to alert us of the traffic.

Original NASA ASRS Text

Title: C172 flight instructor reported a NMAC during climb in VFR conditions.

Narrative: [Student and I] departed straight out and the tower controller gave us a cleared to turn after 6;500 feet. At about 6400 feet; tower gave us the go-ahead to turn left and we cleared the aircraft and turned left crosswind. After wings level on the crosswind the ADSB warning came on and said 'traffic 9 o'clock same altitude'. I immediately looked left and saw a Cherokee less than 1/4 mi on a collision course and immediately took controls and dumped the nose and power to avoid collision. I reported back to the tower that we had an aircraft fly directly over top of us with no reply other than a frequency change a moment later.I believe the cause of the problem was a very busy controller forgot to follow up with Cherokee on the first call to him saying traffic 12 o'clock 6;600 feet after the pilot of the Cherokee said 'looking for traffic'. This lack of communication along with Cherokee doglegging his upwind leg left of runway heading on a straight out departure caused the near collision. The only thing that saved the near collision was the ADSB warning in the aircraft I was flying to alert us of the traffic.

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.