Date: 202110
Local time of day: 1801-2400
Location: ZZZ.ARTCC, US
Flight conditions: Mixed
Weather elements / visibility: 10
Aircraft: Small Aircraft; Low Wing; 1 Eng; Retractable Gear
Operator: FBO
Operating under: Other 61
Flight plan: IFR
Mission: Training
Flight phase: Final Approach; Initial Approach
Airspace: Class E ZZZ
ATC / advisory: Center ZZZ
Reporter organization: FBO
Reporter function: Pilot Not Flying; Instructor
Reporter qualification: Flight Crew Instrument; Flight Crew Flight Instructor; Flight Crew Commercial
Human factors: Communication Breakdown; Workload; Troubleshooting; Time Pressure; Situational Awareness; Distraction
Second reporter function: Pilot Flying
Anomaly: Deviation - Track / Heading All Types; Deviation / Discrepancy - Procedural Clearance; Inflight Event / Encounter CFTT / CFIT
Detector: Automation Aircraft Terrain Warning
When detected: In-flight
Result: Air Traffic Control Issued Advisory / Alert; Flight Crew Executed Go Around / Missed Approach; Flight Crew Took Evasive Action
Contributing factors: Human Factors
Primary problem: Human Factors

Narrative: Student filed IFR Cross country plan to ZZZ via ZZZ ZZZ1 ZZZ with the RNAV Y into ZZZ1. Contact was made with center after being handed off by Departure and the instrument approach was executed with a touch and go on Runway XX. After the touch and go the Instructor and Student were startled by a TCAS/ Terrain warning which led to a deviation from the missed approach procedure. Once contact was re-established with Center the student and instructor were called out for a possible pilot deviation and given the number to call. While the instructor failed to remind the student of their responsibility as instrument pilots to execute the missed approach on an IFR flight plan; due to the Terrain warning both pilots decided to alter course to maintain obstruction and terrain clearance which led to the deviation. Both pilots will be calling the number and starting the recovery process asap; as well as completing FAA online IFR recurring courses.


Second narrative: With an instructor on board; I filed an IFR cross-country flight plan to ZZZ via ZZZ ZZZ1 ZZZ with the RNAV Y into ZZZ1 for a touch-and-go (as stated in the flight plan remarks). Contact was made with Center after being handed off by Departure and the instrument approach was executed with a touch and go on Runway XX. After the touch-and-go; both my instructor and I were startled by a TCAS/Terrain warning which led to a deviation from the missed approach procedure as we turned from the surrounding hills. Once contact was re-established with Center; we were called out for a possible pilot deviation and given a number to call. While the instructor failed to remind the student of their responsibility as instrument pilots to execute the missed approach on an IFR flight plan; due to the Terrain warning both pilots decided to alter course to maintain obstruction and terrain clearance which led to the deviation. Both pilots will be calling the number and starting the recovery process ASAP and completing FAA online IFR recurring courses.


Synopsis: Instructor Pilot and Trainee reported not following the published missed approach procedures on an RNAV approach. The pilots reported after completing a touch and go; they received a terrain warning which resulted in deviation from the procedures.