The book/story was written before 1980 (at least). It centers on a young woman (on Earth) who can read thoughts. She has to hide this fact, because the authorities have discovered that some people have psychic abilities, of different kinds. Some can read minds, some can transmit thoughts, some can do telekinesis. She gets into contact with a secret group of "psions" (not the term in the book/story). Eventually she discoverers that she is a super-high-level "psion", but not before she is caught and sent to a "prison" on the Moon. In the end, they all teleport away with the help of some friendly "psionic" aliens.
Another detail: Young female protagonist's main "psion" friend is a guy who has all the talents, which is unusual and indicates that he is extra powerful. I think he is best at transmitting thoughts. She has a hard time meeting him in person because he is confused about how far from him she is.