Bushing test tap was broken after opening tap cover. Evidence of arcing inside. What could the possible reason for this? And, how to fix it?
You cannot use the bushing without 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 sometimes even transformer fire.
There are some designs (eg.Micafil) where the pin will always be grounded to mounting flange. When you want to test for C&PF, insert 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.