Although Kid was beaten and imprisoned by Kaido after their initial meeting at Kid’s base, his defeat most likely doesn’t mark the end of his importance in the story of One Piece.
We know that Scratchmen Apoo has most likely betrayed the Alliance with Kid, in fact he now appears to be allied or, at the very least, a subordinate to Kaido, as he contacted him to reveal that they had lost contact with Jack. During the conversation, Apoo referred to the Yonko as “Kaido-san”.
Basil Hawkins also joined the Beasts Pirates and became one of the crew’s Headliners.
The fact that Eutass Kid seemingly refused to work under Kaido, is proof that he possesses a rather strong will. I personally think that it is likely for Kid to play an important role in the war against Kaido where he will help the Straw Hat Alliance to take down the dubbed ‘immortal’ Yonko.
I am 100% sure that he wants to seek revenge for what Kaido did to him, and his best option, by far, is to cooperate with Luffy and Law just like they did on Sabaody.
Kid has also been portrayed as Luffy’s counterpart and potential rival when it comes to becoming the Pirate King, but I honestly think that this role is over. Luffy’s only real rival for that title is going to be Blackbeard. I think it is also likely that Kid is going to be on Luffy’s side during the potential final war against the World Government, together with most, if not all, of the other Supernovas.
*Theory by S.