There are a lot of characters called Gloucester (sometimes
spelled Gloster), because the Duke of Gloucester was a title, not a
name. The most famous Duke of Gloucester of all is Richard Duke of
Gloucester, brother of Edward IV, and a significant character in
Henry VI Part 3 and in Richard III, in which play he becomes king.
Humphrey, Duke of Gloucester, is a main character in Henry VI Part
2, and also appears in Henry IV Part 2 and in Henry V. He was Henry
V's brother. There is a third Duke of Gloucester who does not
appear in any of Shakespeare's plays (although the main character
in the play Thomas of Woodstock) but whose widow does appear in
Richard II, which play starts with a trial over who murdered
Gloucester. Interestingly, all three Dukes of Gloucester were
guardians of their nephews Richard II, Henry VI and Edward V
respectively, and they all came to a sticky end. And then there is
the fictitious Earl of Gloucester in King Lear.