The New York State Department of Motor Vehicles site notes that if your registration has past its renewal date then they cannot extend your current registration. They go on to say that you cannot operate a vehicle if the registration is expired. You can renew a registration up to one year after the registration expires though.
You will need to contact the NYS DMV web site for information about how to renew your registration if it has been expired for less than 1 year. You mentioned your car is parked however keep in mind that driving without current registration is an offense which you can be cited for by law enforcement and receive extra penalties for, in case you plan on driving a vehicle that does not have up to date registration on it.
Driving without registration or with expired registration in New York State is a violation of NY Vehicle and Traffic Code section 401. It is a separate violation of law to display on your vehicle an expired registration sticker. If you cannot provide valid vehicle registration, the police can issue a ticket for an unregistered vehicle.
From the information we could find the penalties for a violation of this NY law can be punishable by a fine of not less than $75 nor more than $300 or by imprisonment for not more than 15 days or both. As for just having expired registration of over 60 days but not being cited for driving an unregistered vehicle seems to have a fine of between $50 and $200.
To read about the registration laws of NYS you can go through the NYS Vehicle and Traffic (VAT) laws, especially Title 4 Article 14. We would advise you that we do not have access to the VAT penalty structure for expired registration and have only found the fine amounts above in our research so you should contact the court listed on any citation you may have received for this offense to get information on the cost of this ticket and what all penalties will be assessed.
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