Clarisse, of course, plays quite a significant role in this novel-she is the one who causes Montag to question both himself and the society in which he lives. She's quite free-spirited and looked upon by the "establishment" as different, even to the point of being required to see a therapist, simply because she chooses to appreciate life rather than to "follow the crowd" and have little substance, or meaning, in life like most of the other people in her and Montag's society.
We never know exactly what happens to her, but Montag does ask his wife one day; Mildred, obviously now numb to any real feelings, mentions she might've died in a car accident, but she's not really sure (p. 47 in my print version) and even forgets to tell Montag that she's gone. Montag also asks Beatty about the McClellans; Beatty replies that Clarisse was an "odd duck", a "time bomb." We never find out if Beatty was involved in her mysterious disappearance, though.