Do you want to register your vehicle in another state?
No.
Is it possible to an insurance in another state and keep my vehicle registered in New York?
No that is not possible.
Have you replaced your New York State insurance coverage with out- of-state insurance?
Not yet, I'm seeing if it's possible.
What happens if I do?
The DMV will take action against your New York State registration and driver license even if you move out of New York.
Will I have trouble getting a new license in New Jersey?