If Brexit were a messy and expensive divorce, Nausicaa Delfas would be the lawyer trying to project a serene and unflappable presence to the court — even as her side’s legal teammates were loudly squabbling among themselves.

The Financial Conduct Authority’s first-ever executive director of international, or Brexit head, has had to prepare for heightening political uncertainty without herself becoming political. Since her appointment in February, she has succeeded largely by keeping a low profile.