Cardinal Wolsey (Orson Welles) appears only in a pair of scenes, but they're important… and not just because it's Orson Freaking Welles.
Wolsey is the Chancellor before More—a tough job, considering that the three men who held it sequentially (Wolsey, More, and Cromwell) were all eventually executed. After demanding More's presence at the very beginning of the movie, he pressures him to help force the Church to recognize Henry's divorce. More won't, which prompts Wolsey to say:
WOLSEY: You're a constant regret to me, Thomas. If you could just see facts... flat on without that horrible moral squint. With a little common sense, you could have made a statesman.
In Wolsey's view, More looks at things with a "moral squint"—meaning that he won't confront things as they are, and tries to inject morality into a situation where it's beside the point. Ironically, Wolsey is a cleric, but his loyalty lies with the king, while More is a layman, but his sympathies are with the Church: They're quite the odd couple.
Wolsey wants to prevent civil war from erupting and killing thousands of people—that's why he's trying to pressure the Church into recognizing the king's right to get divorced, so Henry can produce an undisputed male heir. Those are the "facts" he wishes Thomas could see—in his eyes, More is raising an ecclesiastical objection that would only help create a crisis and kill people. When More says he's praying for the king to have a male child, Wolsey seems contemptuous—prayer is fine, but they need to make an effort.
And you know what? He has a point.
In the end, Wolsey fails to force the Church to bend to the king's will. As punishment, the king charges Wolsey with high treason—an act of betrayal on the king's part, really. But Wolsey is already dying, and croaks before he can answer for the charges. On his deathbed, he tells Norfolk:
WOLSEY: If I'd served God one half so well as I've served my King... God would not have left me here, to die in this place.
DUKE: Thank God you're dying here. The King would have you die in the Tower.