2 Samuel 13:20-29

Absalom told his men, 'Wait until Amnon gets drunk; then at my signal, kill him! Don’t be afraid. I’m the one who has given the command. Take courage and do it!' So at Absalom’s signal they murdered Amnon. Then the other sons of the king jumped on their mules and fled." v.28-29
Absolom took matters into his own hands and killed Amnon for raping his sister. David was mad with Amnon for raping Tamar, but David did not punish him. David probably hesitated because:
1.) he didn't want to cross Amnon, who was his first born son and next inline to be king
2.) David was quilty of a similar sin himself in his adultry with Bathseba. While David was unsurpassed as a king and millitary leader, he lacked skill and sensitivity as a husband and father.

Taken from the NLT Life Application Study Bible