I live right on the VA/TN border here in Bristol, so I carry in TN all the time.
Unfortunately, you need a permit to carry in TN, but if you have one, you can carry open or concealed as you see fit.
I have had TN law enforcement try to tell me on several occasions that you cannot carry openly with a permit in TN. They have stated that you could be charged with going armed.So, I have started carrying a small card around with me that quotes the law to educate them:
39-17-1351. Handgun carry permits.
n) (1) Except as provided in subdivision (n)(2), a permit issued pursuant to this section shall be good for four (4) years and shall entitle the permit holder to carry any handgun or handguns that the permit holder legally owns or possesses. The permit holder shall have the permit in the holder's immediate possession at all times when carrying a handgun and shall display the permit on demand of a law enforcement officer.
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.
39-17-1308. Defenses to unlawful possession or carrying of a weapon.
(a) It is a defense to the application of § 39-17-1307 if the possession or carrying was:
(2) By a person authorized to possess or carry a firearm pursuant to § 39-17-1315 or § 39-17-1351;