Well for one,
Joker and the Thief is Tennessee's fight song now. I wish I was joking, but you'll hear it just about as much as Rocky Top.
There used to be a few other things, but it's mostly just canned recorded music and recordings of the PA guy saying "it's thiiiiiiiiiiird doooooooooown" these days. Well, it may not be recorded, I don't know, but it sure feels like it sometimes. It all feesl recored. Welcome to the Jungle, Third Down for What, so on, so forth. At least Third Down for What sort of started at Tennessee, I guess.
They're trying to make everyone sing some song between the 3rd and 4th quarters but that's not really a tradition, just a manufactured thing that hopefully won't take.
The band still gets to play from time to time, but not half as much as they used to.