When an insurance carrier has certified a motor vehicle liability policy under sections 60-529 to 60-531, the insurance so certified shall not be canceled or terminated until at least ten days after a notice of cancellation or termination of the insurance so certified is mailed to the insured. If the insurance is not reinstated by the insured within ten days, the insurance carrier shall provide notice to the department by filing a notice of the cancellation or termination in the office of the department. A motor vehicle liability policy subsequently procured and certified shall, on the effective date of its certification, terminate the insurance previously certified with respect to any motor vehicle designated in both certificates.