Typically even if you are uninsured you can make a claim against the at-fault party in an accident. Your situation seems a bit unique in that you say that the car was gifted to you but it is not registered in your name. Usually when a vehicle is gifted to someone the title is transferred to them and the car is registered in their name.

New York has pure comparative fault laws and you were deemed 30% at fault for the accident, so only 70% of the total damages can be recovered from the other party. A claim can tried to be put in with the other party's insurance company. You can find out what rights your do or do not have as an uninsured motorist at the NYS Department of Insurance.

If you are not the registered owner of the vehicle than it will likely need to be the actual owner who puts the claim in for the damages to the vehicle. If the owner has insurance on the vehicle, check to see if you are covered when driving the car.

If the car was not insured by anyone, than there could be penalties for both you and the car's registered owner. In NYS, a lapse in insurance usually means that there is a suspension of the car's registration and owner's driving license, unless the plates were surrendered to the DMV.

In New York, you can be ticketed, arrested and have your vehicle impounded if you are found driving without insurance. Get a quick quote here for New York car insurance so that you no longer drive without insurance.