You can switch to a new auto insurance company at any time, but to avoid overpaying or violating state law, you do need to watch out for a couple of things. Car insurance policies are often sold for coverage periods of six months or one year. In some cases, you may be charged a fee if you decide to cancel your insurance policy early. You may also be entitled to a refund for the unused portion of the premium. You also want to make sure you have continuous coverage to avoid a coverage gap.