Clare is the daughter of California University's Chancellor Arnold. She is introduced as a privileged, cultured, intelligent and bold woman, who is used to getting what she wants. She grew up in a fictional European country, where her father was an economic consultant and her late mother was best friends with the mother of Prince Carl, her childhood friend who Clare described as "a spoiled rich pain in the butt". Clare's mother passed away while Clare was still young and she and her father ended up in California.
In 1994, Clare is a senior in high school and attends a retreat for the Chancellor's task force, where she rooms with Kelly Taylor. Clare becomes interested in Brandon and wastes no time making her intentions clear. During an evening in which the two of them had wound up alone at his home, she made a series of playful passes at him. Brandon, being a CU student at the time, felt uncomfortable due to the position that Clare's father held, and soundly resisted. Clare later threatened to get Brandon in trouble with her dad, but none of her threats were carried out.
Clare moves into the beach house with Kelly and Donna upon starting UCLA, where she skips a year and begins as a sophomore. It was during this period that she also began seeing David Silver. An early point of their relationship involved her catching him handcuffed to a bed, and deciding to have her way with him. They were interrupted, however, when her father suddenly arrived outside, causing Clare to leave a much-agitated David alone until he was released later on. They also made a X-rated video of each other that was nearly viewed by Donna Martin's parents (though Dr. Martin strongly implies he saw the whole thing and found it amusing). While there was some initial turbulence between them over Clare not telling her dad they were dating, things went downhill in Season 5 when David admitted he still had feelings for Donna, leading to an initial breakup, a brief reunion, and then a final parting of ways between Seasons 5 and 6.
After she and David had broken up, Clare began dating Steve Sanders after she became his math tutor. Though both were playful, it was during this relationship that Clare began to reveal a more serious and sensitive side as she and Steve fell in love. However, at the end of their first year together, Prince Carl came to California determined to win Clare's love. He was ultimately unsuccessful and Steve and Clare remained together despite his interference.
On one occasion, Clare was able to overcome stage fright by looking out at Steve and directing a song towards him.
In another episode, the couple briefly addressed the topic of marriage and where they each stood on it, eventually deciding that they'd simply follow their hearts. As Season 7 wound down, Steve's uncaring mother dumped Clare's father, and Clare (who had spent much the year pissed off at Steve for various things he either did wrong or she inaccurately blamed him for) pushed Steve away once again.
Following their college graduation at the end of the seventh season, Clare reluctantly left Steve—and subsequently, the series—when she accompanied her distraught father out of town, wanting to ensure that he didn't feel alone. Her last on-screen moment was with Steve on the beach.
Clare meets Brandon at her father's task force retreat and becomes attracted to him. She pays him a visit at his house when he's home alone and handcuffs herself to his bed, but Brandon, while attracted to Clare, doesn't engage because of his relationship with the task force and the Chancellor. After Brandon's engagement with the task force ends in Washington, Clare shows up to make another play for him and they hook up, but not before Kelly shows up and Brandon abandons any interest in Clare. Although Clare starts dating David after starting CU as a sophomore, she shows on many occasions that she has genuine feelings for Brandon and really wanted to be in a relationship with him.
David and Clare start dating their sophomore year in college after meeting in a Media Studies class. They have a fun and light relationship, mostly based on sex, but break up when they both admit to having feelings for someone else; David for Donna, Clare for Brandon. They reunite for a while, but Clare breaks up with David during the summer before their junior year. They stay friendly afterwards as part of the gang.
Steve was Clare's longest relationship but her obsessiveness over everything from her schoolwork to her father drove a rift between them. While they stayed together until she left Beverly Hills, the relationship was under constant strain from Clare's issues with her protectiveness of her father. While Steve made an effort to please Clare most of the time, she ultimately chose to follow her father to France and break up with Steve for good.
- „After boarding school, I kinda have trouble believing large groups of women can live under the same roof without killing each other”
- —Clare to Donna
- Clare is fluent in 5 languages, one of them being French