@TheBestUselessGoddess my hunch (and analysis) it will be a new girl, and either a strict teacher or a disciplinary committee members students.
Why?
1) Because the pattern. So far, 1 new girl always released after parody act or any plot whatsoever to integrate the previously new girl in the group. Basically: New girl - kissing/parody/integrating arc - [some rare but exist, actual plot] - [some more parody if the author need to think more material] - [if that is still not enough, hiatus/rest for a week] - New girl again.
The fact that this cycle/week we dont see any rest/hiatus, is means that the author already has the idea, and that highly possibly is a new girl.
2)"Firm". That word, associated with the setting which is a school, means a school rule. If we associate it as a keyword for the new girl, then we know:
In school, there's 2 possible woman whose job is to make the rule stays firm, teacher or disciplinary committee member.
3) it is either Nagano-sensei-like character from TWGOK or Yui-like character from to-Love ru. Which are my favourite girl, I see this as an absolute win!! Lets go!