So I totally just got this from this website this is not my answer but I found it:
Quick Answer
Hamlet hesitates to kill Claudius because he believes that Claudius is praying. If he were to be killed right after praying, when his soul is at its most pure, Claudius would go directly to heaven—and Hamlet wants to be sure he sends him to hell. But Hamlet can't hear what Claudius is actually saying; Claudius admits that he cannot fully repent of his murder of King Hamlet, because doing so would mean giving up his crown. So, technically, Claudius's soul is not pure, and Hamlet could have killed him in this moment, but Hamlet doesn't know this!
Detailed Answers:
Hamlet doesn't kill Claudius at this point because he believes that Claudius is praying. He says that killing the king NOW would be "hire and salary, not revenge!" He simply cannot send Claudius to heaven, where he would surely go were he killed just after praying and purging his sins. He thinks that would not avenge his father's murder, because Claudius killed Old <u>Hamlet</u> without giving him the opportunity to pray, and therefore, Old Hamlet must spend time in hell. Hamlet thinks killing Claudius when he is fit for heaven would be like paying Claudius for the murder of his father. That simply would not do.
The real irony is that Hamlet does not realize that his revenge could have been complete if he had actually killed the king then and there, because Claudius was not really praying. Oh, sure, he was on his knees, but Claudius says that he knows he cannot be forgiven for the murder unless he truly repents, and repentance would mean giving up his crown and queen. So when Claudius says "My words fly up, my thoughts remain below./ Words without thoughts never to heaven go," he is really admitting that he knows he isn't forgiven. If only Hamlet had known, then Polonius, Ophelia, Rosencrantz and Guildenstern, Leartes, Gertrude and Hamlet all could have survived.
This is the website: https://www.enotes.com/homework-help/end-act-3-scene-3-why-didnt-hamlet-kill-claudius-2709
