St. Clare was a follower of St. Francis of Assisi. She presented herself to him as a vocational aspirant, and he made her the foundress of the Poor Ladies, a cloistered branch of his minor brothers.
After her death, the Poor Ladies became known as the Poor Clares. There are thirteen observances of the Poor Clare rule. At least four are represented in the US: Order of St. Clare; Poor Clare Colettines; Poor Clares of Perpetual Adoration; and Capuchin Poor Clares.
One rule of thumb that I’ve discovered is If a monastery is named for St. Clare, it is likely OSC.
New Franciscan Community: Poor Sisters of St. Clare:
Many of the active congregations of Franciscan sisters take St. Clare as a model and patroness. The following is not an exhaustive list:
Franciscan Sisters of the Poor, OH:
Franciscan Sisters of the Eucharist, CT:
Franciscan Sisters of Christian Charity, WI:
Franciscan Sisters of St. Clare, WI:
Sisters of St. Francis of the Martyr St George, IL:
Sisters of St. Clare (began in Ireland in 1619):