C172 instructor reported an near midair collision with another light aircraft on approach to gpm.

Narrative:

The near miss happened about 2.8 miles from nawxy on the RNAV 35 approach into gpm. The student and the instructor (myself) were instructed to report the airport in sight about 7 miles southwest from ergey on vectors to intercept the RNAV 35. About 4.5 miles from ergey the student tried to call fort worth center three times all the way to ergey without any response from approach. (Approach was busy on arrival). As the instructor I changed radios to make sure the controller could hear us and tried to call approach (at this time we are already intercepting the RNAV 35 approach). [On] the first attempt still no response (10 miles from gpm); [on] the second attempt I received a response (7.2 mlesi from gpm/ 3.0 nawxy) we were cleared for the RNAV 35 approach and told to switch to tower on 128.55. During the switch over I got an alert on my ipad from my scout ads-B portable letting me know traffic at 12 o'clock 2 miles same altitude. The student was in the middle of calling tower. During the tower's response to let me know I have traffic ahead I had taken controls from the student and turned left to avoid the aircraft I had spotted after the alert. I was roughly 400 ft. Or less from the aircraft; enough to see the tail number and pilot clearly as I rolled out on a northerly heading off of the RNAV approach path. After landing I went to [the] tower and talked to the controllers to make sense of why the aircraft was heading the opposite direction and same altitude when I was cleared for an IFR approach on an IFR flight plan. The response from the tower personnel was that the other aircraft was already on with approach with flight following. Tower manager had called approach to ask to look into the matter.some contributing factors: 1. Controller was obviously overwhelmed with calls entire time on frequency.2. Controller was not paying attention to my aircraft- I was flying on radar vectors direct to ergey at 3000 [and] the controller did not call out traffic in the pattern right below us; but called the traffic out to an aircraft nowhere near the airport to the north.3. Controller not following my aircraft dumps us off to gpm 2.8 miles from the FAF with no traffic advisories about the multiple aircraft coming out of gky and gpm from ergey to the hand over.

Original NASA ASRS Text

Title: C172 Instructor reported an NMAC with another light aircraft on approach to GPM.

Narrative: The near miss happened about 2.8 miles from NAWXY on the RNAV 35 approach into GPM. The student and the instructor (myself) were instructed to report the airport in sight about 7 miles southwest from ERGEY on vectors to intercept the RNAV 35. About 4.5 miles from ERGEY the student tried to call Fort Worth Center three times all the way to ERGEY without any response from Approach. (Approach was busy on arrival). As the instructor I changed radios to make sure the Controller could hear us and tried to call Approach (at this time we are already intercepting the RNAV 35 approach). [On] the first attempt still no response (10 miles from GPM); [on] the second attempt I received a response (7.2 mlesi from GPM/ 3.0 NAWXY) we were cleared for the RNAV 35 approach and told to switch to Tower on 128.55. During the switch over I got an alert on my iPad from my Scout ADS-B portable letting me know traffic at 12 o'clock 2 miles same altitude. The student was in the middle of calling Tower. During the Tower's response to let me know I have traffic ahead I had taken controls from the student and turned left to avoid the aircraft I had spotted after the alert. I was roughly 400 ft. or less from the aircraft; enough to see the tail number and pilot clearly as I rolled out on a northerly heading off of the RNAV approach path. After landing I went to [the] Tower and talked to the Controllers to make sense of why the aircraft was heading the opposite direction and same altitude when I was cleared for an IFR approach on an IFR flight plan. The response from the Tower personnel was that the other aircraft was already on with approach with flight following. Tower Manager had called approach to ask to look into the matter.Some contributing factors: 1. Controller was obviously overwhelmed with calls entire time on frequency.2. Controller was not paying attention to my aircraft- I was flying on radar vectors direct to ERGEY at 3000 [and] the Controller did not call out traffic in the pattern right below us; but called the traffic out to an aircraft nowhere near the airport to the north.3. Controller not following my aircraft dumps us off to GPM 2.8 miles from the FAF with no traffic advisories about the multiple aircraft coming out of GKY and GPM from ERGEY to the hand over.

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.

Attributes
ACN	1725907
Time
Date	202002
Local Time Of Day	0601-1200
Place
Locale Reference	GPM.Airport
State Reference	TX
Environment
Flight Conditions	VMC
Light	Daylight
Aircraft 1
Make Model Name	Skyhawk 172/Cutlass 172
Operating Under FAR Part	Part 91
Flight Phase	Initial Approach
Route In Use	Vectors STAR ACT.KNEAD8
Flight Plan	IFR
Aircraft 2
Make Model Name	PA-24 Turbo Comanche
Route In Use	Other Flight following
Person 1
Function	Instructor Pilot Not Flying
Qualification	Flight Crew Commercial Flight Crew Flight Instructor Flight Crew Instrument Flight Crew Multiengine
Experience	Flight Crew Last 90 Days 102 Flight Crew Total 780 Flight Crew Type 295
Events
Anomaly	ATC Issue All Types Conflict NMAC
Miss Distance	Horizontal 400 Vertical 0