Tennessee Firearms Association has been active and lawfully formed in Tennessee and with the IRS since as early as 1995.  The state political action committee, Tennessee Firearms Association Legislative Action Committee, is a registered state PAC since 1996 and has decades of public filings with the state to account for its activities. 

In addition, there is an entity that has been in Tennessee for many years known as "Tennessee Gun Owners" or to some simply "TGO".  It entity is known by many for decades as one of the online forums to talk about firearms and has an good reputation among gun owners.

Following the Covenant Shooting, Gov. Lee called for the Legislature to pass a Red Flag law.   That has obviously increased public attention on 2nd Amendment issues in Tennessee and public willingness to be involved. 

On April 19, 2023, shortly after Gov. Lee publicly demanded a Red Flag law, a new entity was formed in Tennessee under the name "Tennessee Gun Owners" - see Secretary of State's Business Search.   This entity has a mailing address on 12th Avenue South in Nashville which appears to be a private mail box at a UPS store.  This entity is sending out mailers asking for money to fight the Red Flag issue and directs people to mail them your credit card number in care of "Chris Dorr".   The recent formation by Dorr of a Tennessee entity appears similar to other organizations set up in other states that some reports also link to Chris Dorr or others in his family.

https://www.cleveland.com/open/2019/08/how-one-ohio-gun-rights-group-aims-to-upend-the-public-debate-by-scaring-republicans.html