Rin doesn't have any significant appearances until episode 4. It focuses more on Hanayo, but Rin still plays an important role in pushing her to join muses'. Initially Rin turns down the idea of joining the group with Hanayo because she thinks she isn't idol material, but in the end she apparently has a change of heart and joins alongside Maki, increasing the group's number to six.
With nine in the main cast she doesn't really get any focus on her character after that for the rest of the season since she sort of got her "moment" with Hanayo in episode 4. I could give a summary of the whole season after that episode but she doesn't get any noticeable development nor plays any notable role until the second season in episode 5.
In episode 5, with the second years (Honoka, Umi, and Kotori) on a school trip and unable to return in time for a live performance at a fashion show due to bad weather, the rest of the group votes for Rin to take on the role of leader until Honoka returns. Rin protests greatly to this and reveals her insecurities with being an idol and a leader figure, refusing to wear the dress that the center would wear for the fashion show. She successfully convinces Hanayo to take the center position instead, but at the last second the rest of the group manages to convince Rin to wear the dress and the performance turns out to be a big success. After this she's much more confident about her femininity and wears skirts to practice instead of pants as she always had before.
For the rest of the season she doesn't have any other development or individual spotlight time like she did in episode 5 though she does take Honoka's position as the group's leader at the very end. There isn't any focus on this part as she had already accepted it some time before, after she got over her insecurities.
Re: Revision
With nine in the main cast she doesn't really get any focus on her character after that for the rest of the season since she sort of got her "moment" with Hanayo in episode 4. I could give a summary of the whole season after that episode but she doesn't get any noticeable development nor plays any notable role until the second season in episode 5.
In episode 5, with the second years (Honoka, Umi, and Kotori) on a school trip and unable to return in time for a live performance at a fashion show due to bad weather, the rest of the group votes for Rin to take on the role of leader until Honoka returns. Rin protests greatly to this and reveals her insecurities with being an idol and a leader figure, refusing to wear the dress that the center would wear for the fashion show. She successfully convinces Hanayo to take the center position instead, but at the last second the rest of the group manages to convince Rin to wear the dress and the performance turns out to be a big success. After this she's much more confident about her femininity and wears skirts to practice instead of pants as she always had before.
For the rest of the season she doesn't have any other development or individual spotlight time like she did in episode 5 though she does take Honoka's position as the group's leader at the very end. There isn't any focus on this part as she had already accepted it some time before, after she got over her insecurities.