Don't let insurance coverage lapse.
Are you switching insurance providers? If not, then the provider will simply reprice your policy once you notify them of the vehicle change. Monthly Payments will be adjusted for the remainder of the policy period. If you pay in full, you will owe any difference (or refund due to you if overpaid).
If you are changing companies. Policies can be canceled at any time. If you're paying month to month, just cancel before you're next payment is due. If paid in full, the company will prorate and refund you the unused portion. Be sure to have new policy with new company effective the day BEFORE you cancel with the old company to avoid a lapse. Remember, everything you do regarding insurance is logged in your CLUE report which is checked by every major insurance company. Lapse can cost you hundreds...