A Fateful Connection

Layna Verity is a mutant and a double agent of sorts. She was visiting London for a while, trying to come up with a plan to sabotage Sebastian Shaw's plans to rule over humans.

Charles Xavier crosses paths with her and unintentionally reads her thoughts. Not thinking much of it, they never see each other again until about over a week later when Charles decides to recruit Layna, but to his surprise, he sees her with Shaw.

Layna gives them whatever info she knows about what Shaw plans to do, hoping they can help stop him. Her and Charles eventually end up seeing each other again and joins the team, continuing her work of trying to help these mutant outcasts avoid a nuclear war and form a close connection with the psychic over time.
(This goes on from First class to Apocolypse)