In Act 4, Scene 3, Claudius outwardly displays an attitude of self-possession when he questions Hamlet; however, his mounting fear and anxiety are soon evident to us by the end of the scene. Claudius betrays his craven nature even as he acts to protect his crown. His prevailing attitude is that Hamlet must die in order for him to have peace of mind.
Claudius knows that he is guilty of fratricide but is unapologetic about his desire to retain the fruits of his evil deed. He knows that his 'offense' is so 'rank, it smells to heaven,' but he wants to keep his queen, ambition, and crown. He questions whether 'one (may) be pardon'd and retain the offence.' So, in this scene, Claudius begins to sense the grave danger of allowing Hamlet to live; Hamlet is a threat to his power. Claudius banishes Hamlet to England for killing Polonius on the pretense that he is ordering such a course of action for Hamlet's 'especial safety.' In actuality, Claudius has ordered the King of England to do his dirty deed for him; the English king is to see to it that Hamlet is killed.
Claudius orders Rosencrantz and Guildenstern to make sure that Hamlet is on the ship to England; he must get there for Claudius' contemptible plan to work. The Danish king feels that he will not be able to rest until Hamlet is dead.
Do it, England,For like the hectic in my blood he rages,And thou must cure me. Till I know ’tis done,Howe'er my haps, my joys were ne'er begun.
In Act 4, Scene 3 Claudius is highly suspicious of Hamlet. Consequently, Claudius has devised a plan in order to both find Polonius' body and secure his own safety from Hamlet as he fears what Hamlet may do to him. He tells Hamlet that he will be sent to England, and sends Rosencrantz and Guildenstern with him to England with letters that he hopes England will obey by killing Hamlet. This plan is quite conniving as Claudius has Hamlet thinking he is being protected after killing Polonius, but his escorts have orders to make sure he is killed.