The Bishop of Carlisle is loyal to Richard out of principle. With the courage of his convictions, he publically speaks up against Bullingbrook’s taking the throne at the moment the man announces that he will do so.
Along with his arguments about the illegality of usurpation, he predicts the whole of the Wars of the Roses (which are explored in Henry IV, Parts One and Two, Henry V, Henry VI, Parts One, Two and Three, and Richard III). He is immediately arrested for doing so. Luckily for him, he is committed to the care of the Abbot of Westminster, who quite agrees with him, and invites him to supper. He is a brave man, quite willing to fight if need be. King Henry leaves him free if he will swear to remain peaceful.