How is Claudius ambitious in Hamlet?
Most of the events in “Hamlet” are triggered by Claudius’s ambition; when we first see him in Act 1, scene 2, his ambition seems to have brought him everything he ever wanted. By poisoning his brother and working his political connections, he secures the kingship for himself and wins the queen for himself (interesting thing to consider: was Gertrude in love with Claudius before the death of King Hamlet? The play doesn’t definitively answer). In Act 3, Claudius counts his ambition among the reasons he killed his brother: “My crown, mine own ambition, and my queen.” His ambition keeps him scheming late into the play: he expertly redirects Laertes’s anger at him onto Hamlet and concocts an elaborate plot to remove Hamlet for good. Ambition drives Claudius’s actions; in a sense, it drives the action of the play itself.
Claudius' ambition forms the heart of the entire play. Claudius is so ambitious, he is willing to kill his brother, the king, and take over his throne. He then marries his brother's wife to cement his hold on the throne. When this Hamlet begins to question Claudius and his actions, Claudius is willing to poison his own nephew/stepson. To protect his plan of poisoning Hamlet, he allows his wife to accidently drink the poison meant for Hamlet, resulting in her death. I'd say Claudius was pretty ambitious since he was willing to kill three members of his own family in order to be king of Denmark.