That route is not as steep as some others. Keep your pack weight reasonable and you should be fine.
Be sure to call ahead for reservations for all shelters. You can call as early as 30 days prior to the start of your hike. You can get all the info you need
here.
Hopefully you'll have good weather to enjoy the view from Clingman's Dome. It's worth stowing your gear for a bit at Icewater Springs Shelter and walking the extra mile up the AT to Charlie's Bunion, an absolutely great view, weather permitting.
Are you staying at LeConte Lodge or Shelter? Even if you are only staying at the shelter, you can still get snacks and a few souvenirs at the Lodge, so it's worth checking out and bringing a few dollars cash.
Enjoy the Tennessee side. It tends to be greener. I don't say that out of state pride, but simple science. Tennessee is on the north slope, gets less sun, and therefore retains rainfall better than NC. But once you're in the valleys, you'll get great green hardwood forest on either side of the AT.
Best of luck!