and should I deliver the plates?
yes, you must turn in your plates.
How do I avoid a lapse of insurance?
Remember this simple rule: no insurance, no plates!    keep your vehicle's mailing address and valid driver's license with the DMV  they have liability coverage from a company licensed by the New York State Department of Financial Services and licensed by the New York State DMV. Out-of-state coverage is never acceptable on any vehicle registered in New York