Most insurance companies will offer a renewal or transfer discount if you are able to provide evidence of prior insurance coverage. Some are so generous with this discount that they allow up to a 30 day lapse in coverage. When shopping for new insurance you should notify the agent or company that you had previous insurance even if it was more than 30 days ago. You may still be entitled to an extra discount.
You should make sure your car's registration is not suspended due to this gap in insurance though so that the buyer of the vehicle does not have a problem registering it in their name. Also in some states you are unable to register another car until your vehicle's suspension is over due to being without insurance.
You can get a car insurance quote here to see how much this discount could save you.