Yes, Tess is unfortunately and tragically very much dead in The Last of Us TV show and will not be returning unless in a flashback.
Her noble sacrifice ensures that Joel and Ellie can escape. However, it means that she will not see the end of their journey.
Fortunately, she is replaced by another beloved character in the next episode, who is being played by a very famous and beloved sitcom actor.
Tess dies at the same point in both The Last of Us TV show and video game. She does not return to either at a later stage, so fans will surely miss her presence in later episodes.

How Does Tess Die in The Last of Us TV Show?
Tess blows herself up in the Capitol building after she drops a lighter into a puddle of gasoline and grenades. She does this to stop the Infected from chasing Joel and Ellie.
However, even if Tess had not blown herself up, she reveals moments beforehand that she is infected after an altercation with a Clicker in the museum.
Of course, while Tess is gone, Joel and Ellie’s journey must carry on. So, make sure you know exactly when each episode of The Last of Us drops to see its conclusion.
Had Tess somehow managed to escape from the explosion, which she absolutely did not, she would have succumbed to the infection.
She is also attacked by an Infected who puts her tendrils into her mouth as she attempts to light her lighter. This is the final nail in the coffin, as there is no way she could have survived that.

It is worth noting that Tess dies in a slightly different way in the video game. In the game, she, Joel, and Ellie are not pursued by Infected but rather by FEDRA.
In The Last of Us game, Tess does get infected. However, instead of blowing herself up, she dies in a shootout with FEDRA soldiers.
You can see how Tess dies in The Last of Us video game below:
How & When Does Tess Get Infected in The Last of Us TV Show?
Tess gets infected when fighting the Clickers in the museum during episode two of The Last of Us TV show.
She disappears during the fight while Joel and Ellie fight a Clicker. It is presumed that during this time is when she is bitten by the Clicker.
If you pay close enough attention, you can see the Clicker that Tess fights has blood all around its mouth, likely from where it bit Tess on the upper torso.

Why Did the Infected Kiss Tess in The Last of Us TV Show
The Infected kisses Tess in The Last of Us TV show as it is trying to connect its tendrils to the ones already growing inside of her.
Because she is infected, the Cordyceps will have begun spreading its tendrils inside of her. The Infected connect via these tendrils, so the kiss was to create that connection.
You can learn more about exactly how the Cordyceps virus began by understanding Mycology and its surprisingly realistic connection to The Last of Us TV show.
Unlike in the game, the infection is spread through the tendrils created by the Cordyceps virus. These come out of the Infected’s mouth.
We see these tendrils also come out of an Infected earlier in episode two when the Mycologist is studying it.

When the Infected bite a human, the tendrils inside of their mouth spread the Cordyceps through the wound into the bloodstream.
However, the tendrils also function as a way for the Infected to connect with one another and create a hive mind.
This is how they know that Joel and Ellie are inside the Capitol building. The tendrils of a dead Infected in the building spread across the ground where Joel, Tess, and Ellie are standing.
So, the Infected isn’t kissing Tess for fun. It is actually attempting to finalize her transition into one of them by connecting his tendrils with hers.
When Does Tess Die in The Last of Us TV Show?
Tess dies at the very end of episode two of The Last of Us TV show. It comes only minutes after she, Joel, and Ellie reach the Capitol building.
In the final moments of the episode, Tess drops her lighter into the gas poured across the ground and sets herself and the pursuing Infected ablaze.