Welcome to Tennessee!
With a valid carry permit, you're good to go in TN, because of reciprocity.
Hank's side note: TN constitutionally recognizes all/most out of state permits, but there can be differences in law. Check here
for state reciprocity agreements.
We do not mandate concealed carry, but it is highly recommended.
You may not carry in any place that is posted (which now may include the simple "gun-busters" circle & slash symbol, and nothing else).
If you carry in a place that is not posted, but management requests you to leave because they've become aware you are carrying, you must do so. Failure to do so
may subject you to a criminal trespassing charge. Discretion is the better part of valor.
You may not carry while consuming alcohol (or vice versa- consume alcohol while carrying).
Hank's side note: bar/restaurant carry was recently approved in TN. See caveat above about posted locales, but if it is not posted or otherwise against the law, you are good to carry.
You may carry in groceries/package/liquor stores where alcohol is sold for off-premises consumption, as long as they are not posted.
State parks are OK. Though there may still be signs up saying something to the effect "No Guns Allowed", they no longer apply to permit holders.
City & local parks are a hodgepodge of can & can't. Most larger city parks are prohibited; most small municipalities are OK- but they are to be posted if prohibited.
We have a castle doctrine. It's not ideal, but better than it was. If you are attacked you do not have a duty to retreat.
Please check the Tennessee Firearms Association's online forum for more information.