Final answer:
Claudius plans for the English king to execute Hamlet upon his arrival in England as part of a secretive plot to eliminate him.
Step-by-step explanation:
Claudius's plan for Hamlet upon his arrival in England is a deadly one. He doesn't intend for Hamlet to be arrested or kidnapped. Instead, Claudius's trap is to have Hamlet executed upon his arrival. He arranges this by sending letters to the English king, instructing him to kill Hamlet as a favor owed to Denmark. This treacherous plot is a pivot from outright confrontation to a more secretive form of elimination, showing Claudius's cunning and desperation.