It usually takes about 5 to 10 business days to receive the new replacement regarding the address change. However, if you didn't pay the $17.50 replacement fee, then DMV wil not just send you a new updated one via. (For expired driver's license, you have to apply for a new one only at the DMV office, not online.) If you went to update it at a local DMV, then you should've gotten it by now.
From the DMV website: We mail your license, learner permit or non-driver ID to the address we have our records. Allow 2 weeks to receive the document. ****If your document is not delivered two weeksafter the date the document was processed, you can send a question to us online, call the DMV or visit your local DMV office*** So just call the NY dmv, and they'll probably have to mail you a new one since it probably got lost in the mail or something. Also make sure it's been 2 weeks not counting weekends. Either way call them.
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