You cannot get a new VA license without proving residency, and in any case, VA state law requires you to notify the DMV of any change of address. In most states, driving with a license that has incorrect information is equivalent to no operators license, and you can be charged if you are even stopped in a random check.
but there are plus sides. VA is also a state that tries to keep you forever and make you pay state taxes, unless you take specific steps to prove that you are no longer domiciled in VA. If you keep a drivers license, that counts as a 'tie' to VA. If you never intend to live there again, then cut the ties.