I'm a little at a loss to understand this term "compressor stall". I'm going to assume you are all referring to an engine surge. The indications of a stall will start with ITT/EGT/TGT rise as the airflow brakes down and could lead to a reversal of airflow (a surge) which would be indicated by a large bang possibly accompanied by flame from either or both the engine exhaust and or inlet. With the surge will come a fluctuation in N1/N2/N3/NG and temperature which may also be the only indication if the stall doesn't develop into a surge.
There is a great video of a Thomson 767? swallowing a bird and suffering a surging engine afterwards. I had something similar on the L1011 on a training flight after a touch and go with simulated engine failure.
The Engine which had been at idle for the last 10 minutes decided to complain after being accelerated for the take off. In the cockpit the only indication we had was a banging so loud we thought we had come under fire. The Aircraft was and RAF tanker fitted with a camera which I used to check the engines and was somewhat concerned when I swung it onto no.3 and saw the engine coughing it's innards out of both ends.
Appropriate checklists were completed and we scrubbed back to the squadron for tea and biscuits. The next day in the engine servicing bay we looked at what was left of the HP compressor. Not Much!
My advice. If it miss behaved to the extent that you had to shut it down, think very carefully before relighting. Of course we can imagine scenarios where you might consider relighting a shutdown engine but in a hundred years of aviation they haven't happened very often.