Tennessee along with your home state of New York should suspend your driver's license if you fail to pay the speeding ticket you received in Tennessee.
If you do pay the Tennessee speeding ticket you will be out the fine amount but it will not affect your New York driving record. On the flip side if you ignore the TN ticket then you will end up with penalties from both Tennessee and New York.
States share information about moving violation convictions drivers receive or a driver's failure to comply with an out-of-state ticket. Many states place an out-of-state violation on your driving record and assign it points however New York does not in most cases.
The New York State Department of Motor Vehicles (DMV) does not record convictions of minor moving traffic violations by NYS non-commercial licensed drivers in other jurisdictions, except traffic offenses committed in the provinces of Ontario and Quebec, in Canada.
Now if you fail to take care of an out-of-state ticket then New York will take action against you. Both TN and NYS are members of the Non-Resident Violator Compact (NRVC) which requires member states to suspend the driver's license of those who get traffic tickets for moving violations in other states and fail to pay them.
The NYS DMV says specifically that they will suspend your New York driver's license if you fail to answer a ticket for a moving violation in any state except Alaska, California, Michigan, Montana, Oregon or Wisconsin (states that are not members of the NRVC). Furthermore, your license will remain suspended until you answer the ticket.
Back in Tennessee they say if you fail to appear in court or pay for a traffic ticket by the court date it will result in a default judgment against you, higher court costs, and state penalties. You also will be charged with the additional offense of Failure to Appear which comes with its own separate fines and court costs on top of your speeding ticket fine amount.
Another penalty for not paying your Tennessee traffic ticket is that the Tennessee Department of Safety will be notified by the court to initiate suspension of your license in TN. The court will also notify the NYS DMV about the failure to appear or pay for the ticket so they can suspend your license.
We have heard from people that have failed to pay tickets in Tennessee from out-of-state and they indeed say their driver's license was suspended in TN and their home state plus Tennessee sent their unpaid ticket to collections.
If you do not follow through with the speeding ticket in Tennessee not only will your license to be suspended in TN and NYS (which when your home state suspends your license it is not valid to drive on it in any state) but you will start to get letters and calls from a collection agency. Tennessee will continue to request payment of the fines and possibly mark this on your credit report as non-payment and affect your credit rating.
If your driver's license gets suspended it will be hard to keep car insurance on your vehicle since automobile insurance companies normally require that you have a valid driver's license to keep your car insurance policy in effect. Even if you manage to keep your auto insurance policy in effect, if your car insurance company sees the suspension on your driving record it is bound to affect your car insurance rates.