Even if your car insurance is with a national insurance company, you will need to find a local representative of that company in your new city and state. Many people have the misconception that they can continue with the same insurance agent if they are moving out of state, but that isn't quite accurate. If you are relocating you will need to switch agents, as laws and insurance prices vary from state-to-state.
You can find a new insurance agent in your new city or state by contacting your current insurance agency. The people at your current agent's office should be able to give you the names of agents that will work with you in your new city. It is important to contact your new insurance agent prior to your relocation, so that you can move to your new home with complete insurance coverage in that city and state. You may have to pay less or more on the same policy when moving to a new city, for example, South Carolina car insurance is more than Iowa car insurance (under some insurance plans) because Iowa has what is determined as safer drivers than South Carolina.
What you will pay for insurance will depend on your insurance agent and your location.