The test tap cover works as a grounding device for the tap and should be tightly screwed while the bushing is energized. Always.
Most likely the cover got loose or the tap leaft uncovered while the bushing was energized and overvoltages appeared between tap and flange.
If the tap was damaged, I would replace the bushing.
I dont think you need to replace the bushing as such. You may not be able to do C2 on it. But if overall Tan Delta and capacitance is fine, you are okay with this bushing. You cannot install an online Tan Delta or PD system vide this tap. If crack has not caused any oil leakage, then there is oil one layer shorted. I would not worry.
You cannot use the bushing with out test tap grounded. In such a case the last grounding foil of condenser core will be floating and the voltage developed between the last foil and grounded flange will cause arcing that may lead to bursting of bushing and some times even transformer fire.
How to fix? - I would recommend replacing the bushing. It may be possible to remove the bushing and have it sent back to the factory for repairs - may be.
Due to the risks of the bushing failing and taking out the transformer, replacement is the sound strategy.
The damage may have occurred during installation or if you have Doble tests performed on the bushing. It may have been due to over zealous removal or installation of the bushing cap or someone attached a lead to the pin for testing and inadvertantly broke it.
I would think that at the least the broken pin should be extracted and a new one installed in the cap. The insulation around the pin socket looks damaged but as it is grounded in service it would only be a problem during testing or if this was used for a bushing potential device. If the pin is not fixed the arcing may continue and you wouldn't know about it until.....
There are some designs(eg.Micafil) where the pin will always be grounded to mounting flange. When you want to test for C&PF, inserts a tool and isolate the pin from the grounding flange. I do not think this belongs to that group.
If you desperately want this bushing, check continuity of broken end of pin to ground . If it shows continuity, you can put it back in to service. But the problem is you will not be able to monitor the PF. These days no one will keep such a bushing in service for long, without monitoring PF.