To simply purchase a handgun you do not need any permit. This could possibly even give you a heads up if your prior record will come up. Since you do not need a permit to have a handgun/firearm inyour home/business either.
Many times expungments don't show up on background checks and you have to follow through with presenting court documents to show the expungment. So if possible it may be a good idea to contact the court and go ahead and get those records.
You can see a bit of the information on getting a TN Handgun Carry Permit on the state's website here.
Basically you will need to take a Dept of Safety certified safety class. You can check your local paper or I thing there may be sources on here where classes are available. The cost can range anywhere between $50 - $100. Upon successful completion you will be given a certificate that is valid for 6 months.
Within that 6 months you go to a Drivers License testing center to fill out an application.Take the certificate and proof of USCitizenship or Lawful Permit Residency.The cost of the permit is $115 and is non-refundable and due at the time of the application. They will direct you to a place to have your fingerprints taken.
Then it is basically sit and wait. The state has 90 days to issue you the permit or give you a reason for denial. You can appeal a denial.