What are the possible checks that must be done if the transformers incoming breaker has tripped
If the tripping happens at the transformer commissioning stage, check the polarity of the CTs neglecting their S1 and S2 stickering. If the tripping happens in normal working time, check the terminations at earthing the star point. The third one may be relay malfunctioning.
One thing you should know is that if all things are normal, circuit breakers trip to clear fault in their zone of protection. So if the incoming breaker for a transformer trips, check that the settings of the breaker are right for the transformer load and the breaker has no inherent fault. Then check your transformer visually, there could be a short circuit physically or through conductive dust. Ensure the transformer oil level is okay. If it’s a big transformer, check if Buchholz relays settings are okay, complete transformer tests for dissolved gas analysis, insulation resistance, continuity, oil quality, polarization index, check temperature and oil winding indicator relays, check for water condensation inside oil and finally filter transformer oil. Extend your check to transformer neutral resistors for large transformers.