You have to apply for Section 8 housing in whatever state you live in, it goes by your current address. So, you could move to New York and apply or apply for the list in Tennessee: https://thda.org/renters/waiting-list and get a voucher and then "port" it to New York: https://www1.nyc.gov/site/nycha/sect...rtability.page but technically you either have to live somewhere and apply from that address (which in your case now would be Tennessee) or go somewhere, find a place to live, and then apply from that address in your new location. Each state runs their own Section 8 program for the Federal Government (they get varying amounts of money from the Government depending on how many people they have that need housing in their state).

If you have a place to live now; I'd apply to Tennessee and get in the program, get a voucher, and then see about porting it to New York if you think you might have a better chance of a place there. However, New York is more expensive to live in than Tennessee so you might want to consider that, too.