This word means "existing, living, or occurring at the same time." It is not a synonym for either present-day or modern unless no other question of time is involved and the inference is "contemporary with now." If the time frame of reference is that of Queen Elizabeth I, then a lecture on contemporary drama would mean plays of Elizabethan times. If the frame of reference is to drama of the present day, the time of Elizabeth II, then contemporary would mean "now." Because contemporary means what it does, it is an error to use it with more (meaning "to a greater degree"). It is impossible for something to be more contemporary; probably what is meant is more modern."An Elizabethan play in modern costume" is clearer in meaning than "an Elizabethan play in contemporary dress."
Dictionary of problem words and expressions. Harry Shaw. 1975.