Prior to the apocalypse, Tennessee was a U.S. state. Kenny mentions that he and his family were driving back from Memphis, the second largest city in the state, after visiting his sister-in-law, just before the apocalypse began.
At some point, around the first year or so after the apocalypse began, a group of survivors led by William Carver and Luke began to found a community within an abandoned business park in Tennessee. They set up their main base of operations in the largest building located on the site, a former Howe's Hardware store.
Clementine, alongside Sarita, Kenny and the remains of the Cabin Group were captured by William Carver's group and transported to their community called Howe's Hardware in Tennessee. They remain at the hardware store until they escape later after killing Carver and escaping from his group. They later encounter Parker's Run, a historical outdoor museum located a possibly long walk away from the hardware store. Soon after a while, Rebecca, one of the cabin members, was preparing to give birth to her baby. They manage to get her up to an observation deck, where the group defends it in order to avoid being devoured by walkers and to help Rebecca deliver. Soon, Rebecca succeeds in delivering her baby, which she soon named it Alvin Jr., named after one of his possible fathers, Alvin.
After either staying just one night or for a few days, depending on the player's choices, the group leaves Parker's Run and head out, possibly walking for another day or two. It is unknown if Clementine’s group left the state by the end of "Amid The Ruins," but it is assumed that they are still in Tennessee as walking for a day or two from Parker’s Run may land them somewhere around central or eastern Tennessee. By the time the group had reached the Unfinished House in the next episode, they are confirmed to have journeyed over the state line into North Carolina.
In "No Going Back", if Clementine goes with Jane back to Howe’s Hardware, which was cleared out by the walker horde, Tennessee is seen once again. It is also seen in flashbacks in Season 3. Otherwise, Tennessee would no longer make an appearance.
In "Home Sweet Home", Maggie reveals to Daryl that she and Hershel were living in a community in Knoxville, Tennessee with Georgie. After Georgie heard of a survivor city out west, she went to check it out with her bodyguards, Hilda and Midge. However, Maggie has not heard from her and soon after, the community in Knoxville fell, forcing her and Hershel to flee.
Sarita - Bitten on the arm by a walker outside of Howe's Hardware (Caused, Alive) Arm chopped off by Clementine and bitten by multiple walkers outside of Howe's Hardware (Alive, Determinant) Head axed by Clementine outside of Howe's Hardware (Zombified, Determinant), or mercifully shot in the head by Kenny in Parker's Run (Zombified, Determinant).
Vitali(likely) - Stabbed in the nape by Jane and shot in the head by Kenny.
Jane - Hanged herself after learning she was pregnant (Alive, Suicide), later then either shot in the head by Clementine (Zombified, Determinant) or left to remain as a walker in Howe's Hardware. (Determinant)