In the comics, Hulk left Sakaar to travel back to Earth with his forces to seek revenge against the Illuminati, which led into the World War Hulk storyline.
Since the Quinjet didn’t make it out into space, it’s unclear just how Hulk ended up on Sakaar.
The last time we saw Hulk in Avengers: Age of Ultron, he had flown away from the battle against Ultron in the Quinjet so he could keep Black Widow safe from him.
Whatever the circumstances, it sounds like he’s already asserted dominance over the other fighters, like Korg and Miek.