You can apply for a new certificate of entitlement before your car goes back, that way you won’t have to waste a month paying and claiming back car tax.
One thing though is do not let your certificate be stamped by the post office as this invalidates it and you will have to apply for a new one the following year, un-stamped you can use it without end for taxing your car year after year, only when you change car do you have to apply for a replacement.