A "dandy" is a male who pays a great deal of attention to his clothes, and makes sure that he always looks smart and fashionable.
A "master" might be a schoolteacher, or, from the perspective of a servant or slave, the person that one serves.
Thus a "dandy master" might be e.g. a very smartly dressed schoolteacher.
On the other hand, "dandy-master" might also be a slang term in an activity with which I'm not familiar.
What context did you find it in?
Student or Learner