Richard Rich is a law graduate of Cambridge, a learned fellow and a friend' of Thomas More. While he is unemployed, More suggests that he takes up a teaching appointment, a proposal which he declines.
His desire and ambition to get rich quickly make him dishonest, disloyal and ultimately a traitor to Thomas More. He allows himself to be used by Crownwell to entrap More. He contributes immensely to the eventual execution of Thomas More which climaxes the plot of the play. Rich's closeness to More puts him in a unique position to serve as a principal witness against More in his trial. More gives him the gift of a silver cup offered to him by a female litigant and it is this cup which Rich makes available to Crownwell as a damaging exhibit in the trial of More.
In a sense, Richard Rich serves as a foil to More's character and this contributes to the development of the plot. The contrast in their characters is crucial to the plot. Whereas More believes that integrity is constant, Rich holds the opinion that 'Everyman has his price'. More's all-trusting nature which leads to his taking Rich into his complete confidence sets the stage for Rich's subsequent betrayal of his 'friend'.
Richard Rich is, therefore, very important to the development of the plot.