Clara Tremblay is a fiction.
She'd tell you the facts, but she can't quite sort it out. Side effect of changing jobs like socks and names to match. After a time, even you start to believe the tales you spin. But it's a necessity. Work an unsavory job, learn some unsavory secrets, and people want you dead and quiet.
The tale changes with every telling, but the consistent bits speak of Lemnos, bodyguarding, and a fair bit of illegal trade. She's spoken of family connections without dropping names. Whatever the truth, she's seen her share of the world and knows how to adapt to a new place. She's a fair hand with a sword and has no problem using alternatives to fair play.
Taking a job as an instructor seems a nice, safe way to earn a living, and maybe she'll get a student or two that isn't completely hopeless.