from the DMV website
What can I do if my New York State inspection expires while my vehicle is in another state?
Determine if an expired out-of-state inspection is a violation of law in that state. Ask the authorities if a NYS inspection extension sticker prevents a ticket for the violation. A NYS inspection extension allows you 10 days from the date the vehicle returns to New York State to get a NYS inspection done.
Allow 14 days for the DMV to process and mail your extension sticker. You will need it before you return your vehicle to New York.
To receive an inspection extension, send the following information
your name and current out-of-state mailing address
the year and make of your vehicle
your NYS vehicle plate number
your inspection sticker number and expiration date
Mail the information to
NYS DMV Bureau of Consumer and Facility Services
Inspection Extension
P.O. Box 2700-ESP
Albany, NY 12220-0700
When you receive your extension sticker, do not put the extension sticker on your windshield while your vehicle is out of state (keep the sticker and the instructions in your vehicle to show to an out-of-state police officer). The sticker is not a guarantee that a police officer will not issue a traffic ticket.
see it here at http://dmv.ny.gov/inspection/inspection-requirements