Fortune Favors the Sparrow by Rebecca Connolly

Mischief is as mischief does…
Clara Harlow is perfectly content with her life as a teacher of art and French at the Miss Masters Finishing School, so nothing startles her more than to discover that the school is far more than it seems, and its purposes more complicated than anything she could have imagined. She finds herself accepting an assignment from the highest powers in England to use her talents for a particular mission: to impersonate the ward of the late Duke of Kirklin, gain access to the estate, and to discern how a strip of the Kent coastline there is being used against the security of England.

The present Duke of Kirklin, George Russell, better known as Hawk, does not know what to make of the appearance of the former ward of his late uncle, but he is captivated by her. Her skills in art are unlike anything he has ever seen, and her company grows more agreeable with every passing day. His boring, bachelor life grows less and less appealing, and the company within his walls more perfectly suited for the place than he ever dreamed. What could possibly go wrong?