CCW Question

I have a question regarding my current CCW. I'm not sure where on the forums to ask.

I'm currently issued out of Hampton VA but the license itself is non-laminated and too large to fit in a standard wallet. I've recently moved to a city whereas my father has his CCW and it's a standard hard laminate to carry in a wallet. Am I able to "transfer" or get my CCW re-issued by my resident city so it's easier to travel with?

Change of Address – Section 18.2-308.011

The clerk of a circuit court that issued a valid concealed handgun permit shall, upon presentation by the permit holder of the valid permit and written notice of a change of address on a form provided by the Department of State Police, issue a replacement permit specifying the permit holder's new address. The total amount assessed for processing a replacement permit due to a change of address shall not exceed $10, with such fees to be paid in one sum to the person who accepts the information for the replacement permit.

Would the new license be issued by my current city?