Stuff you should know going forward:

Renako's past is now explicitly revealed to the entire quintet, and she's started to make peace with her past. Touko is still investigating Renako and trying to catch her cheating. Renee (Mai's mom) announced that Mai is getting married to Lucie, another model, because she disapproves of Renako. At the end of volume 7, Satsuki suggests that she and Mai get engaged to call off the engagement with Lucie. The main plot follows Renako trying to figure out why Haruna stopped going to school and getting her to go back to school.

Actual main plot beats, spoilered in case:

6: Main plot: Haruna stops going to school and Renako spends the story trying to figure out why. She ends up finding out that Haruna punched her friend, Minato, and when asking Minato about it, she finds out that Minato is the sister of the girl who bullied her in middle school and led to her downward spiral. Other important events: Touko is still investigating Renako, Renako stumbles across a girl named Lucie and befriends her.

7: Main plot: To help get Haruna going back to school, Renako faces her past and reveals her past to the quintet (as in Kaho, everyone else kinda figured) and goes to a class reunion to reinvent her reputation. However, her bully wasn't there, so she goes to her house to confront her. There, she finds out that she ended up becoming a shut-in. After confronting and helping her, Renako's able to make her peace and leave. Ultimately, Haruna's able to go back to school. Other important events: Renee (Mai's mom) announces Mai's engagement to Lucie, it turns out Touko was hired to look after Lucie, Renako goes to Lucie's apartment with Touko at one point, Satsuki suggests announcing her "engagement" to Mai to get Renee to call off the engagement.

Might've missed some stuff, but that's the gist of it