A move is not a does not give you the right to terminate your current car insurance. You may only switch your car insurance at the end of the agreed insurance period. Most contracts run until Dec 31 with a 30 day notice period.
Please note: If you move, inform your car insurance company of your new address immediately. This is prescribed by the so-called notification requirement.
Moving might change the insurance premium for your car as objective and subjective risk characteristics are adjusted to your new address.