The character above is Tatenashi Sarashiki.
Unfortunately, she won't be featured in Anime this time, since she first appears from Vol.5
I'd think that they would put a scene in the epilogue of EP12 briefly hinting her appearance in hopefully upcoming 2nd season.
(Some action by her would be great, but I think a full face shot or even just a silhouette might be possible)
She is a 2nd grade student in IS Academy.
(Since it is treated like high-school, the 1st, 2nd, and 3rd grades in IS Academy is equivalent to 10th, 11th, and 12th grades in highschool - the junior-high school would also have 1st, 2nd and 3rd grades, with 3rd being equivalent to 9th grade of highschool)
Although there are many 3rd grades students, she holds the title of the president of student council in IS Academy. The basic rule in Academy is that the strongest student takes the position, meaning Tatenashi is currently the strongest student.
And she is strong...
Ichika was able to hold about 10 mins against Houki.
Laura, being a combat speciallist with ample live-combat experience, can overpower Houki.
And Laura is no match for Tatenashi...
When Ichika had a match with Tatenashi (martial arts) he got his ass kicked.
(He stopped counting from 16th hit while recieving her combo because he lost consciousness.)
She later turns out to be Russian representative IS pilot.
(Remember that most heroines are representative candidate.)
She is also the 17th generation leader of Sarashiki family, a secret organization fighting the Phantom Task (this is the evil organization) from below the surface.
Using her power of the president of the student council, she assign herself as Ichika's roommate, but with a good reason.
After being notified of imminent threat to Ichika (and his IS), she puts herself in a position to protect him all the time. (hence the roommate setting)
When the threat is gone, (at least temporarily) she returns to her own room again, but occasionally visits Ichika's room unannounced.
(She apparantly mastered the way to pick his room door)
She appear as a care-free and mischievous character, (while being immensly strong) and Ichika views her as just that - mischievous and uncomfortable person who seemingly enjoys teasing him.
(Since Ichika tends to be overly polite to person senior to him - especially toward girl, even if she is just a year older than him - he has hard time coping with her.)
Ichika considers her to be way out of his league, but she appears to have some feeling toward him.