It depends on why you moved to NC and how you work in NC. That is, whether you work from home or in the employer's facility and the nature of the work you do.
If you work from home, for your convenience, you are subject to NY tax. Your employer is most likely aware of this rule and will withhold NY tax.
Telecommuting. If you work outside the state as a job requirement, you are only subject to New York State income tax on the days you work in New York. But if you work outside New York for your own convenience, you are subject to New York State income tax on all your income. Pennsylvania, Nebraska, Delaware and New Jersey have the same rule. For guidance see: http://www.journalofaccountancy.com/issues/2009/jun/20091371.html
Here's a link to New York's memorandum on its "convenience of the employer" tax doctrine regarding non-resident telecommuters: https://www.tax.ny.gov/pdf/memos/income/m06_5i.pdf
