I can't recall the name of a novel where a young human woman takes care of a group of children who may have psychic powers but the government does not know what their abilities are or when they will manifest. When the woman identifies that a child has an ability she notifies the authorities who take the child away, most like to be dissected for experimentation.
After the first child with an ability is taken away the young woman decides to protect the rest of the children. Most of the children display abilities. The book may be set on a starship due to some of the references.
When the young women goes out to socialize she wears a dress of twigs and leaves as she does not have a full body tattoo which is the current vogue.
There was an alien, a green being that may have been like a pet. The book itself had a green cover, and may have the word "green" in the title.