if NJ didn't send you a calculation you can use this form
https://www.nj.gov/treasury/taxation/pdf/current/2210.pdf
to avoid the same thing for 2024, ask your employer if it will withhold NJ taxes. They are not required to do so in most case. if they do, you'll need to have extra withheld to make up for the first part of the year when nothing was withheld. the target is 100% of your 2023 NJ taxes (it should be line 50 of NJ form 1040. if they won't all you can do is make estimated tax payments to get to the 100%. however, estimated tax payments only count when made so you will be subject to penalties for the early part of 2024.
see this link for making estimated tax payments
https://www.nj.gov/treasury/taxation//njit20.shtml
in fact the required payment is the smaller of 4a or 4b from the 2210 for 2024. however knowing what your 2024 taxes will be is sometimes not possible.
