Polonius is still spy on Hamlet, he doesn’t trust Queen Gertrude. He thinks she will lie to them to protect her son. And so does King Claudius, he agrees Polonius idea and wants to spy on Hamlet and Gertrude. This is a foreshadowing on the relationship between King Claudius and Queen Gertrude.
Hamlet has a chance to kill Claudius when he is praying, but Hamlet chooses not to. He thinks Claudius doesn’t deserve go to heaven, he wants Claudius go to the hell. Hamlet will kill Claudius when he is enjoying life or doing