Yes, as mentioned in previous replies above, nobody sends you a sticker because you bought an atv/utv, or any other off-road vehicle with an engine size over 50cc.
(Edited to add: Some dealers may do this as a service to customers).
It is up to the owner to go to their county clerks office with their atv/utv title and receipt and fill out a form, pay a small fee, and the clerk will issue a sticker to be applied somewhere on the frame. The sticker says "TDR" and has a number on it.
TDR stands for Tennessee Department of Revenue, and the number is tied to your form you filled out so they can look it up if they ever have too.
As for the practical side of it, you will find very few off road vehicles that have the sticker. If you get pulled over it is not going to be for an officer checking for your TDR sticker. Although maybe on federal land they may be more diligent about checking everything, like your sticker and spark arresting devices.
At the edge of my farm is a choke point dirt road entrance into the Wolf River bottoms where atv/utv's pass through 365 days a year, 24 hours a day (I got used to the noise long ago, lol).
Every now and then law enforcement will set up there and do a check-point for atv/utv riders coming and going. They arrest tons of people for DUI, weapons and drug posession, and impound those vehicles when they make an arrest. But I have NEVER seen them check for the TDR sticker.
I would say that if you have been riding for years and never had a problem about not having a TDR sticker, you can keep riding and it is very unlikely to ever be an issue.
As mentioned in my previous reply, my atv was bought from an deceased persons estate and there wasnt a title available, and no way to get a title in TN, so no way to apply for the sticker. I had an officer who was looking for a stolen atv pull me over. He mentioned the sticker in passing, but that was not anything he was concerned about and released me without any citations.
But if you like to "cross the T's and dot the I's" you can run down to your county clerks office and get your sticker.
Personally, I wouldnt worry about it.