Ah
the female protagonist who hasn't been getting a lot of screentime. Some even consider Megumi the female main lead, but I will acknowledge that when she earns the same amount of spotlight and appears on the jump collaborations.
I find female characters that don't sugarcoat their words to the main character very refreshing. In all the times she has tasted his dishes, she has never told him that it's adequate for the situation, and that was exactly what Souma needed to hear for him to improve. Except for his entrance exam, which I didn't take completely serious because she said it with a chibi face, and one little tooth. That is Tsukuda telling us to not to freakout over the rejection. That aside, she has never directly tried to get him expelled. For someone at her skill level, it would have been very easy to just challenge Souma to a shokugeki. Knowing his recklessness, he would've accepted.
Erina and Souma are actually pretty similar despite what is on the surface. They both have the common goal of aiming for the top (first seat), enjoys playing cards even during the hell training camp, and can be totally badass/cocky when they need to be. She's also not as spoiled as people think she is. Sheltered, sure, but everything she owns at Tootsuki was earned with her cooking skill. Whenever she needs a new kitchen, she just does a shokugeki risking her Elite 10 seat. It's probably hard not to be cocky when everyone is telling you how amazing you are all the time.
Chapter 9's title is "The Ice Queen and the Spring Storm." Erina has been referred to several times as the "Ice Queen" and Isshiki described Souma as spring. We've seen her thaw out, hastened after witnessing Souma in the Autumn Elections.
Some would call her a "tsundere" though I don't agree completely with those labels. If she is a tsundere then she is an incredibly intriguing and well written one because normally I find "tsunderes" really annoying.
Anyway it's obvious that Tsukuda has a lot planned out for her. Whether or not that involves crushing defeat, we'll see. At the end it would be interesting for her discard her ojousama status after learning more about Joichirou. She might even have her own special-of-the-day shop, putting the pressures of the Nakiri family behind her.