Driving a vehicle without a valid driver license can affect your insurance rates, but an expired license may be treated differently than not having a license at all. For one thing, most states allow a 30 day grace period to renew an expired license, and being stopped within that period will probably not result in an fraction against you at all, simply a warning by the officer involved to get your license renewed as soon as possible. Even if you do receive a ticket during this period, getting your license renewed before speaking with a judge or court clerk will usually be a cause to withhold adjudication, which means the offense does not show up on your driving record at all.
On the other hand, driving on a license that has been expired for 90 days or longer will probably result in a traffic offense and points against your license. In this situation, your car insurance premiums may increase because of the accumulated points against your license, not because of the expired license charge. Keep in mind too that an expired license is far different than driving without a license, which carries harsher penalties and may result in forfeiture of your vehicle license.
If your license is expired, get it renewed as soon as possible. If you are involved in an accident and your license is expired by more than 30 days, the insurance company may dispute the claim onthe basis that you were not legally entitled to be driving at the time of the accident.