Gloucester Timeline and Summary

Gloucester mourns the death of Henry V, accepts his role as Lord Protector of England (acting caretaker till Henry VI is old enough to rule), and proclaims Henry VI King.
Gloucester tries to check on the Tower to make sure it's doing okay, but is refused entrance on Winchester's orders, so he argues with Winchester instead. Their men start to fight, and it has to be stopped by the Mayor of London.
He has a dispute with Winchester in Parliament, again their men start to fight, and again the Mayor intervenes.
Young King Henry tries to make peace, which sort of works for the time being.
Gloucester gives Henry advice to be crowned in France, and we see how much Henry respects Gloucester—he remains important in Henry's plans and coronation.
Gloucester recommends peace and plays a strong role in the negotiations. He recommends that Henry VI accept the offer of marriage with the Earl of Armagnac's daughter, who is rich and a good bet politically as well. Henry agrees.
Gloucester strongly recommends against dumping the Earl of Armagnac's daughter for Margaret. Henry VI does it anyway, and in our last glimpse of Gloucester in the play, he is fearing that it will all come to grief.