As ThoughtCo explains, by 1529, Pope Clement was no longer Charles V's prisoner, but Rome was still under the control of the Holy Roman Empire. The pope sent an envoy, Lorenzo Campeggi, to try to mediate a solution that would upset neither Henry nor Charles. While both Henry and Catherine made their appeals in Campeggi's court at first, soon Catherine stopped appearing at the hearings, and ultimately the court adjourned without stating a verdict and never reconvened. This meant that Henry's hopes of an annulment were basically done for, and he wasn't pleased with that one bit. Henry's representative in his negotiations with the pope had been his chancellor, Cardinal Wolsey, who negotiated through years of the pope's hemming and hawing. Henry removed Wolsey from his position as chancellor and charged him with treason. Wolsey, however, died before his trial could begin.
Henry replaced Wolsey as chancellor with not a clergyman, but a lawyer, Thomas More, the guy who invented the word "utopia." If you've read or seen the play A Man for All Seasons, you know that things don't go well for More, either. More, a devout Catholic, refused to take an oath to support Henry's divorce and marriage to Anne Boleyn. Like Wolsey before him, he was charged with treason, but he lived long enough to be executed. The Catholic Church named him a saint for his loyalty to the faith.
