In Act IV, Claudius as a king (that is, a figure with ultimate earthly authority) tries to protect and preserve the public morality embodied in the social order, ensuring that transgressor - in this case, his nephew Hamlet - must be punished for murder. This kingly decision would have to be irrevocable, and Claudius would have to treat Hamlet just like any other subject. However, this public morality clashes with Claudius' personal morality. Being a murderer himself, he is afraid of Hamlet and what he might find out. So, he wants to just get rid of him, sending him off to England, while arranging for his murder too. The king and the offender in him have to come to terms with each other, but it doesn't go smoothly.
