It is often possible to change your state coverage while keeping your current insurer, given that company is also licensed in your new state of residence. This information can be had by contacting your insurer. If keeping your current insurer is not possible, you must end your contract before you can start a new policy with a different company. This can be done by sending your insurance agent a car insurance policy cancellation request.
Though some states actually offer multiple methods for establishing financial responsibility, or coverage, most give you only option: registering for a state-licensed liability insurance policy. Each state differs here and there but, for the most part, the basic liability insurance coverage required in all states in the same.
