The Ministry of Magic

Your character's name:   Claire Bishop
The job they want: "Auror Consultant." She would be in the ranks of the Aurors, but also in charge of checking efficiency and correcting discrepancies between conduct and policies. She can also be of assistance in the training of new Aurors.
Why they'd be good at it: The American Ministry has some concerns about the British Ministry. They've transferred Claire to the U.K. (the British were in need of talent) to look into some disappearances of American artifacts that have most recently resurfaced in the U.K. Claire has worked in the Auror office in America, and is an accomplished duellist. She passed her Auror training with flying colors, and has been working directly under the American Minister, so she is definitely (if not over) qualified.