It seems to me a wealthy duke should be able to arrange excellent teaching for Clarisse, even if the first teacher hired from outside was a failure. Though that being said, a monastery specialising for educating youths for the civil servant examination would have a number of suitable teachers and long traditions for that specific purpose, not to mention a library with every relevant book. Discussions and teamwork with other students would also be beneficial. If the royal prince is going to attend such a monastery school, then there's no doubt it's the best place. Hard to say if Clarisse is doomed to fail without going to the monastery school, but it's possible.