From the Super Mario Wiki
Kate (Japanese: ケイト Keito) is a character in the Game Boy Color version of Mario Tennis as well as the Nintendo 64 version of the game as one of the four transferable characters. The others are Alex, Nina, and Harry. She also made an appearance in Mario Tennis: Power Tour as a coach.
She wears a tank top, mini-skirt, bracelet, headband, and tennis shoes all colored pink, similar to Princess Peach's sports attire. In Mario Tennis, her hair and eyes are also pink. In Mario Tennis: Power Tour, she looks similar to what she looked like in Mario Tennis, though a little different; even though her tank top, mini-skirt, shoes, bracelet, and headband are still all pink, she has blond hair and blue eyes instead of pink hair and eyes. She and Harry have a friendly rivalry of sorts (emphasis on the friendly), however she actually acts flirtatious towards Harry when describing how he was at wall practice back in the day. At one point in the game, she gives a teasing Harry a push with her rear end, taking advantage of everyone tightly lined up behind them, causing him to lose his balance and knock down everyone behind them.
Kate is the only one of the "Big Four" coaches (Alex, Harry, Nina, and Kate) who you get to play against at one point, although your "matches" against her are net play lessons.