The phrase "take up an appointment" means to begin or assume a new role or position. In this context, "take up" is the appropriate choice because it explains starting or accepting a new appointment. To take over means to assume control or responsibility for something. To take on can mean to accept a challenge or responsibility but the sentence does not suggest that he is accepting a challenge but just a new appointment. To take up means to start a new role or position. To take off means to depart or to remove oneself from a place.