In order to unlock the new area, you need to enthrall the girls at the school. Doing that will progress the plot and eventually give you access to the new area.
is the principal able to be enthralled shes the only one in the school that says "i don't want to talk to her right now" instead of mentioning a later version i had the talk with her about her daughter then talked to her daughter and that's all i can find
Basically, the Principal is connected to her daughter so as you continue speaking with and progressing with her daughter, you'll unlock more content with the Principal.