Cranmer (Cyril Luckham) is the Archbishop of Canterbury—the second man in charge of the Church of England (under King Henry VIII) and the principal leader of that church.
Cranmer acts as a judge in More's case, asking him pointed questions. He doesn't play a huge role in the movie, but he and More have some snarky back-and-forth. Check out this piece of dialogue, in which the Bishop asks whether he and the others who have signed the oath are damned:
BISHOP: So, those of us whose names are there, are damned, Sir Thomas?
MORE: I have no window to look into another man's conscience. I condemn no one.
BISHOP: Then the matter is capable of question?
BISHOP: But that you owe obedience to the King is not capable of question. So weigh a doubt against a certainty and sign.
MORE: Some men think the Earth is round, others think it flat. It is a matter capable of question. But if it is flat, will the King's command make it round? And if it is round, will the King's command flatten it? No, I will not sign.
Mary Queen of Scots would later kill Cranmer for being a Protestant—he was burned at the stake for heresy. Man, those 1500s were bloody times.