Kings' Gambit

Summary
To get this quest you must have completed Ring-a-Ding-Ding. Re-entering the Vegas Strip, you will be approached by a NCR Trooper (unnamed) who will tell you that you have an important message from Ambassador (Dennis Crocker). This will start the quests needed to get the quest King's Gambit.

Crocker tells you about all the violence in Freeside, this being caused by "The Kings" led by The King. What you can do is choose to kill the whole Kings Gang, or talk to Colonel Hsu in McCarran Camp about the resources he sends to Freeside, Hsu will make a deal with The King for trade that he will stop the violence on NCR citizens in Freeside for exchange that Freeside will get food, water, and supplies instead of just NCR soldiers receiving the supplies. Pacer, The Kings "right hand man" will be against the deal in "The Kings School of Impersonation" with the NCR, he will try to kill everyone there (don't shoot him it will make the Kings hate you, have the NCR finish him).

Another way to stop the violence without killing or framing anyone of the Kings is to get on the King's good side. You can do this by completing the G.I. Blues quest an ask him to stop violence against the NCR. He will mention it will be a tough job but he will do it. However, if this option is chosen he will also state that this makes you even and you can't choose any of the other rewards for G.I. Blues anymore.

Edit-I received the quest after completing the quest, "Things That Go Boom".

Bugs
Bug: If you choose to deal with the The Kings via ultimatum with a squad of NCR troopers, you will not be able to complete the quest as Crocker will register that you killed King instead of following quest orders then killing him.

The quest will be failed and you are then handed the next part of the chain.