You will probably get a strange look down here trying to turn in an old plate, you will be asked, oh you want me to throw it away for you? (no receipt) and into the trash it goes…

TN does not require you to turn in your plates,

Nor does NJ. While it’s a good idea to turn-in your old plates (and get a receipt for them), it’s not required.
The motor vehicle law in Tennessee changed in 2024 and it states:
"If a registrant has not surrendered his certificate of registration and registration plates or obtained motor vehicle liability insurance within 90 days from the date of cancellation of motor vehicle liability insurance, the director shall suspend the driver’s license of any such registrant."
As for New Jersey, they do not require you to surrender your plates if you cancel your insurance but intend to keep the car, but you must cancel the registration. However, you must surrender your plates if you are selling the car, junking it, or otherwise taking it out of service permanently.
So, the best advice then is to call your local Department of Motor Vehicles and get the rules and laws as it applies to your location…
Well in late 2024 I sold a vehicle (took title only to dmv) and went down to the dmv to do it and they never asked for the old plate or registration and I still have both, and all I did was email the ins agent and said cancel the ins on said car, he did no issues…
Also in March of this year, my son totaled out his Civic (single car and no property damage), while in the hospital emailed the ins company and said to cancel the vehicle(didn’t even have the police report yet), never said why and it was never asked, just renewed and vehicle is off and no issues, also I kept the old plate…The tow lot just sent a letter saying it would be sold at action, I’d already talked to them and cleaned out the car the day after the wreck and we talked about how it would all go down…
But yes, if you have plates on a vehicle and it’s driven, you do have to have ins now, they have started cracking down on that… But had a guy that bought non drivable 93 Mustang and put plates on it (codes) and never added ins to it, no issues, just sold it couple weeks ago…