No, Gi-Hun will not become the new frontman
I’ve seen a lot of ppl theorizing that Gi-Hun will become the frontman. But we don’t even know if In-Ho wants to retire as frontman, or if the squid game organization is even hiring for any leadership positions? The premise of season 2 is that Gi-Hun won’t let go of how upset he is about the games, whereas the frontman (In-Ho) wants our guy to gtfo to America to hang out with his daughter.
So I don’t get why so many theories rely on the assumption that Gi-Hun is being recruited for the frontman role or even some other role in the organization. I don’t get the impression that the games are short-staffed (although maybe they are after episode 7). We also don’t have any reason to believe that former winners typically become staff or leaders at the games.
And the central conflict between Gi-Hun and In-Ho has nothing to do with Gi-Hun’s employment. The reason In-Ho is going after Gi-Hun is to persuade him that the games are an inevitable result of human nature (all the players are basically race horses in In-Ho’s opinion), so that Gi-Hun stops trying to expose or take down the games. The purpose of all of this is to prove a point and neutralize a threat, not mint a new leader.