TRACON controller reported a military training flight was assigned 4;000 feet; but stopped their cli...

Narrative:

Aircraft X had been in the radar pattern at ZZZ. He questioned his climb out while on approach (as it was amended on his last approach and wasn't reiterated on this approach). After listening to the tape he was given heading 260 and 4;000 feet by the local controller and read it back correctly. Upon checking in with the departure controller; he said he was at 3;000 feet with request. The departure controller took his next request and turned him on downwind. After listening to the tape; aircraft X questioned whether he should be at 3;000 or 4;000 feet; but was stepped on. I heard the low altitude alert go off; saw aircraft X at 3;100 feet inside the antennae area- where the minimum vectoring area is 3;500 feet. I instructed the controller to climb aircraft X immediately; he did and aircraft X climbed.we discussed earlier opening up final sector. If we had; all of our controllers would have been on position. We also discussed giving the final to radar east; but it would only have put all/most of the traffic on the other scope. In the future; I would insist that more of the military aircraft do approaches at an air force base in our airspace; not most of them at ZZZ. One was sent there; but I would send more. This would divide the workload better.

Original NASA ASRS Text

Title: TRACON Controller reported a military training flight was assigned 4;000 feet; but stopped their climb at 3;000 feet and flew below the Minimum Vectoring Altitude.

Narrative: Aircraft X had been in the radar pattern at ZZZ. He questioned his climb out while on approach (as it was amended on his last approach and wasn't reiterated on this approach). After listening to the tape he was given heading 260 and 4;000 feet by the Local Controller and read it back correctly. Upon checking in with the Departure Controller; he said he was at 3;000 feet with request. The Departure Controller took his next request and turned him on downwind. After listening to the tape; Aircraft X questioned whether he should be at 3;000 or 4;000 feet; but was stepped on. I heard the low altitude alert go off; saw Aircraft X at 3;100 feet inside the antennae area- where the Minimum Vectoring Area is 3;500 feet. I instructed the Controller to climb Aircraft X immediately; he did and Aircraft X climbed.We discussed earlier opening up final sector. If we had; all of our controllers would have been on position. We also discussed giving the final to Radar East; but it would only have put all/most of the traffic on the other scope. In the future; I would insist that more of the military aircraft do approaches at an air force base in our airspace; not most of them at ZZZ. One was sent there; but I would send more. This would divide the workload better.

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	1658559
Time
Date	201906
Local Time Of Day	1801-2400
Place
Locale Reference	ZZZ.TRACON
State Reference	US
Environment
Light	Daylight
Aircraft 1
Make Model Name	Military Trainer
Operating Under FAR Part	Part 91
Flight Phase	Cruise Initial Climb
Route In Use	Other Instrument Approach
Flight Plan	IFR
Person 1
Function	Approach
Qualification	Air Traffic Control Fully Certified
Experience	Air Traffic Control Time Certified In Pos 1 (yrs) 19
Events
Anomaly	ATC Issue All Types Inflight Event / Encounter CFTT / CFIT

TRACON controller reported a military training flight was assigned 4;000 feet; but stopped their climb at 3;000 feet and flew below the minimum vectoring altitude.