It would be best to ask in the Tenn side of the forum, but my understanding is that Tennessee isn't a "traditional open carry state" but is a "shall issue" state that issues a carry permit that allows both open and concealed carry. I would suspect the permit is 21+ but wouldn't swear to it.
39-17-1351. Handgun carry permits.
(a) The citizens of this state have a right to keep and bear arms for their common defense; but the general assembly has the power, by law, to regulate the wearing of arms with a view to prevent crime.
(b) Except as provided in subsection (r), any resident of Tennessee who is a United States citizen or permanent lawful resident, as defined by § 55-50-102, who has reached twenty-one (21) years of age, may apply to the department of safety for a handgun carry permit. If the applicant is not prohibited from purchasing or possessing a firearm in this state pursuant to § 39-17-1316 or § 39-17-1307(b), 18 U.S.C. § 922(g), or any other state or federal law, and the applicant otherwise meets all of the requirements of this section, the department shall issue a permit to the applicant.
(c) The application for a permit shall be on a standard form developed by the department. The application shall clearly state in bold face type directly above the signature line that an applicant who, with intent to deceive, makes any false statement on the application commits the felony offense of perjury pursuant to § 39-16-702. The following are eligibility requirements for obtaining a handgun carry permit and the application shall require the applicant to disclose and confirm compliance with, under oath, the following information concerning the applicant and the eligibility requirements: