North Carolina and New York are both members of the Drivers License Compact (DLC) and Non-Resident Violator Compact (NRVC). As members of the DLC it means that if you were convicted of the speeding offense in North Carolina that the NC courts would then inform the New York Department of Motor Vehicles of this conviction.
The NYS DMV does not record convictions of 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. Therefore, except for traffic convictions in Ontario and Quebec, out-of-state traffic convictions are not added to your New York State "violation point" driving record so points are not assessed.
So if you are convicted of the NC speeding ticket the NYS DMV will be notified however they will not add it to your motor vehicle record or assign you points. Without the out of state speeding ticket being on your driving record it is unlikely your insurance company will find out about the offense and thus it would not normally affect your rates.
We mentioned that both NC and NY were also members of the NRVC. This agreement requires member states to suspend the license of a driver who gets a traffic ticket for a moving violation, such as your over speeding ticket, in another state but fails to pay or otherwise legally comply with the citation.
The NYS DMV discusses this by stating that your New York State license will be suspended 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. Likewise, drivers from any state, except those from the six states listed above, will have their driver licenses suspended in their own state for failure to answer a moving violation summons in New York State.
This is why it is important to take care of out of state tickets. Some motorist mistakenly think they can ignore out of state tickets and they will go away however usually a state continues to come after you for the fine amount of the ticket and contact your state's DMV so that your license is suspended until you comply and take care of the citation.