According to www.handgunlaw.us it looks like you are good to carry in our state on the PA permit.
But I urge you to do a lot of checking before you come. Tennessee is a gun friendly state but, it has some odd laws that a lot of other states do not have. Such as, not being able to carry into a restaurant that has a license to serve alcohol.
Also, you can not carry in any state or municipal parks.
Go to http://www.handgunlaw.us
to check the do's and don't's of Tennessee carrying.