In the latest chapter of the Manga, Chapter 147, Souma beats Eizan in a shokugeki. The terms were for Eizan to stop destroying the Polar Star Dorm, but does Souma get to also usurp Eizan's position in the Elite 10 as the no. 9 spot (I believe Eizan is number 9 but not sure) because he beat him in a shokugeki? Or is there not enough information to answer?
Each side must lay out their "compensation", or something they must give up if they were to lose the challenge. Both sides must agree that the compensation of the duel equate with each other.
I guess the battle will only save the polar star dorm. Originally, whatever they bet before the Shokugeki is what they'll get when they win. This means if Souma wants to dethrone him, he'll need to propose another battle asking for the position if he wins.
But we'll see on the next chapter what would be the outcome.