The entire universe was gunning for Thanos in Avengers: Endgame and Dave Bautista reveals that Drax will be left unsatisfied by the fact that he did not finish off Thanos himself. Drax the Destroyer was introduced in Guardians of the Galaxy as someone who sought revenge on Ronan the Accuser for the death of his family. It's revealed at the end of the movie that Drax's real target is Thanos.
At the end of Avengers: Infinity War, Drax fought Thanos (and was originally going to have a one-on-one fight with him) but he was snapped away along with half of all living beings in the universe by the Infinity Gauntlet. The present-day version of Thanos was beheaded by Thor at the start of Avengers: Endgame and the time-traveling version of Thanos was destroyed by Tony Stark, who used the Infinity Gauntlet to erase him from reality.
Thanos might be gone, but Drax is due to return in Guardians of the Galaxy Vol. 3. The question of Drax's future in the MCU was brought up in an interview with Bautista in GQ. The actor believes Drax will need a new foe to focus on in the next movie, as he will have been left unsatisfied by the fact that he wasn't personally responsible for the demise of Thanos. Bautista said:
"I don't know. I think he’s going to be a little unsatisfied he didn’t kill Thanos himself. I thought about that a long time ago. James [Gunn] is super creative, and he's also a fan so he will dig through and come up with a new villain and something for Drax that I'm sure people will appreciate. He’s a genius."
The role of Drax the Destroyer in the Guardians of the Galaxy movies is similar to that of his comic book counterpart, with the exception of the comic version of Drax originally hailing from Earth. The comic version of Drax has actually succeeded in his goal of killing Thanos in the past, as he tore Thanos' heart out of his chest during the Annihilation crossover. Drax's entire story arc has revolved around his mission to avenge his family, but the sacrifice of Tony Stark was too important to the story of the MCU going forward to allow Drax to finish off Thanos himself.
The question now is where the next Guardians of the Galaxy movie will take the character. Bautista believes that writer-director James Gunn might come up with a new villain for Drax to face in the future, but the drive for vengeance won't be the same as it was when Thanos was the villain. Guardians of the Galaxy Vol. 3 is still in the early stages of development and isn't expected to be released until 2021, but it's possible that more information about the film will be revealed during the Marvel Studios panel at San Diego Comic-Con 2019.