Clarisse doesn't take up a lot of space in this short story; she's mentioned in Section 4, and Section 5 is told from her point of view. Alcée's wife, she is conveniently out of town during the storm; her absence enables him to cheat on her with less fear of being found out. So we kind of have to read between the lines to figure out who she is and what she's like.
Since she and Alcée have young children, she is probably relatively young. We know Alcée appreciates a pretty lady, so she's probably fairly good looking. They can afford for her to go on vacation to another town for a while, so they must be fairly well off as a couple.
And Clarisse herself? Let's take a peek at Section 5, the only part of the text that comes from her point of view:
As for Clarisse, she was charmed upon receiving her husband's letter. She and the babies were doing well. The society was agreeable; many of her old friends and acquaintances were at the bay. And the first free breath since her marriage seemed to restore the pleasant liberty of her maiden days. Devoted as she was to her husband, their intimate conjugal life was something which she was more than willing to forego for a while. (5.1)
First, the word choices here reveal that Clarisse may be more formal and proper than some of the other characters. When discussing her, the narrator doesn't use dialect or slang; instead, she uses ladylike language like "doing well," "charmed," "agreeable," "pleasant," "devoted," and "intimate." These are polite nothings, or pleasantries, like "nice to meet you" or "fine weather we're having." The narrator uses pleasantries to describe Clarisse's life, and they tell us little about what's really going on in her head. Unlike Calixta, who is sewing when we first see her, Clarisse is moving in "society." She has more time on her hands and should have fewer worries. But does she?
Second, this passage shows that Clarisse is not all that eager to get back to her nice husband, a husband who – according to Calixta at least – is pretty cute and good in bed. So what gives? Why does Alcée turn Calixta on but turn Clarisse off?
Clarisse claims that she is "devoted...to her husband," but what does this mean? She doesn't use the word "love." Does she not enjoy sex ("intimate conjugal life"), or does she not enjoy being a wife and mother? There's something about her life that's just not that fulfilling – much the way Calixta doesn't realize she's missing out on her own full sexual potential.
Third, being apart from Alcée is a state Clarisse describes as a "pleasant liberty," a nice freedom. If being apart from him feels like freedom, then being with him must feel in some way like imprisonment. It seems like being married and at home stifles Clarisse. Only when she's on vacation is she able to take her "first free breath since her marriage." How might years of marriage and motherhood change a woman?