TN honors all other states permits..."as if issued by TN" However TN only issues permits to those 21 and over.
I am not aware of any court cases or legal opinons on whether an out of state permit issued to someone under 21 is valid in TN for sure or not.
But if you do not have a permit, you can not have any loaded firearm in your vehicle.
If you do have a permit you can have a loaded handgun and a long gun can have a loaded magazine/tube as long as a round is not in the chamber.
Any firearm can be transported if unloaded without a permit. To be considered unloaded the firearm must "not concealed on or about the person and the ammunition for the weapon was not in the immediate vicinity of the person or weapon."