If you do apply for PIP and you are awarded the enhanced rate for the mobility section then you are exempt from paying any car tax. You have to apply via a letter but the link will take you to the page that gives you the details.
If you are awarded the standard rate for the mobility section then you can have 50% off a years car tax bill.
I'm both cases if you have already paid car tax the DVLA will refund you either all your money or the amount less the 50%.
However, if you are renewing your car tax and want the 50% reduction, you have to pay the whole 50% by cheque I'm one go – you can not pay monthly via direct debit.
If your car needs to be taxed – you must always tax it, even if you are getting the full exception.