Just because the other driver’s license expired does not mean that they do not have insurance. Get 2 estimates and see if they will pay. If not, then turn over to your insurance for uninsured motorist’s coverage. They will pay for the repairs, minus your deductible, and then go after the other driver for repayment.
DISCLAIMER: David J. McCormick is licensed to practice law in the State of Wisconsin and this answer is being provided for informational purposes only because the laws of your jurisdiction may differ. This answer based on general legal principles and is not intended for the purpose of providing specific legal advice or opinions. Under no circumstances does this answer constitute the establishment of an attorney-client relationship.