When you change your Drivers licence to another state does your previous state auto insurance cover you when you travel out of your state if you didn't change it?

Most likely not since most states have different laws for auto insurance (the policies change). When you change your address, you will most likely have to start a new policy. Also, if you do not have the correct address on your insurance policy, they can deny coverage (especially for theft) because the price of your policy is based statistics for your area