Hi kjkjzhang,
Based on your description, you are a full year NC resident, hence need to report all income earned while a full year NC resident.
Your TX employer may not have registered to collect and remit NC income tax, so you need to manage NC tax liability on your own.
North Carolina Department of Revenue - Estimated Income Tax
https://www.ncdor.gov/taxes-forms/individual-income-tax/estimated-income-tax
You can remit via Form NC-40, Individual Estimated Income Tax online or pay by check. In general, North Caroline has a flat tax rate of 5.75%.
Hope the above helps.
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