First the carry permit in TN is for Handguns only.
39-17-1307. Unlawful carrying or possession of a weapon. —
(a) (1) A person commits an offense who carries with the intent to go armed a firearm, a knife with a blade length exceeding four inches (4"), or a club.
If you read further
(a) It is a defense to the application of § 39-17-1307 if the possession or carrying was:
(1) Of an unloaded rifle, shotgun or handgun not concealed on or about the person and the ammunition for the weapon was not in the immediate vicinity of the person or weapon;
If you have your HCP you may transport a long gun with magazine loaded and empty chamber
Lastly per forum rules
(14) LONG GUN CARRY IS OFF-TOPIC: This web site is focused on the right to openly carry properly holstered handguns in daily American life. We do NOT promote the carry of long guns. Long guns are great! OCDO co-founders John & Mike and most of the members of this forum own at least one long gun - but due to urban area issues of muzzle control, lack of trigger guard coverage, and the fact that the long gun carry issue distracts from our main mission to promote the open carry of handguns in daily life, we will leave long gun carry activism in the capable hands of the future founders of web sites about long gun carry. Exception: This rule does NOT apply to discussions about long gun carry in jurisdictions such as California which ban handgun carry and thus require long gun carry as a matter of public policy.