Clotho was the gang leader of the all-female Sisters of Fate gang in Kaede.
The most notable thing about the gang is that they are the opposite of the Brothers of Destiny gang, who have a love/hate relationship. Despite bitterly hating each other, the two gangs need one another for certain synergistic purposes. They also have very different ideologies.
Her name is a reference to the Greek goddess Clotho, one of three sisters in the Moirai (Ancient Greek for "Fates").