Not only as a notable homeroom teacher of B-Class, she's also known to have friendly and easygoing personality, thus, she is acquainted with many people of all ages.
Advanced Nurturing High School Edit
Chie claimed that she and Sae are friends back when they were students at their old school. However, she may have been exaggerating as Sae denies they were close and even reprimands Chie for her interaction with Kiyotaka as Chie disregards this.
Tomonari is one of her fellow teachers, they don't have any direct interaction in the anime so the exact nature of their relationship is unknown.
In the light novels, Chie and Tomonari are known to be quite close and consider each other best friends. They are able to talk with the other on a personal matter, such as about each other's love interests with ease.
Class 1-B Edit
Honami is one of her students, they are on good terms with Chie acknowledging Honami's intellect. In return, Honami respects her as such though she does consider her to be eccentric because of her drinking.
During the cruise, the two get a massage together and discuss the students of other classes they should watch out for and while Honami is put off by Chie's erratic behavior, she seems to see her teacher is right about watching Kiyotaka.
Class 1-D Edit
Despite not having any interaction in the anime, it appears that Chie had suspicions about his intelligence. This was seen in a talk with Honami where she recognized him as a person from D-Class to watch out for the most.
In the light novel, they had a unique type of relationship, where she was shown to tease and flirt with him despite being a teacher. Kiyotaka, however, was shown to be a little put off by her antics and eccentric nature.