Driving without insurance is illegal in New York State and comes with its own fines and other penalties.
NYS law requires you to have insurance to drive on the roadways there. If you are convicted of operating an uninsured motor vehicle or permitting another person to be operate your uninsured vehicle, your license will be revoked for at least one year. The same penalty applies if the New York Department of Motor Vehicles receives evidence that you were involved in an accident without being insured.
Some revocations require you to pay a civil penalty before your application can be accepted for a new license. This includes revocations for No Insurance or Uninsured Accident. These violations come with a $750 civil penalty.
The civil penalty is an additional monetary payment over the normal fine amount. NYS Vehicle and Traffic law 319 notes that being caught without insurance is a traffic infraction and upon conviction you may be fined not less than $150 or more than $1500 or may be imprisoned for not more than 15 days or both the fine and jail time.
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You mentioned that your driver's license is from New York while your registration and license plates are from Virginia. If you have moved to NYS and have become a resident then you are required to obtain NY plates and insurance.
The NYS DMV states that if you are a not a resident of NYS, a vehicle registration from your state of residence is valid in NYS. If you become a resident of NYS, you have 30 days after you become a resident to register your vehicle in NYS. If you are a resident of NYS and you get a vehicle from another state, you must register the vehicle in NYS.
To get a car registered in New York you must have valid NYS liability insurance on it. The NYS DMV does not allow you to use proof of insurance from another state under any circumstances. | 
