Should I do another PhD?
It is not possible to give a concrete answer without knowing which area in Chemistry you did for your PhD. I assume you are from India. There are other options for you to consider irrespective of your field of research.


Try to get an INSPIRE Faculty position, which is not really a faculty position in usual sense.
Apply abroad which will increase your chance of finding a similar field at least statistically.


I don't think appearing GATE once again is a good idea. Also why don't you try industry, there are plenty of jobs for chemists, once again its hard to say for sure without knowing your area of research.