David is still dying, but can't just shut up and get it over with. No, first he has to give Solomon some advice: follow the lord and you'll be fruitful and multiply, blah, blah, blah. Because the main purpose of his speech is to tell his son who to exact revenge on: first Joab the general for his disloyalty. Then Shimei, the relative of Saul who yelled curses on him, because even though David promised not to hurt him, Solomon made no such vow. Then David dies rather undramatically, though I'm sure this isn't the last we'll hear from him.
So, Solomon establishes himself as king. One day, his brother Adonijah, who you'll remember tried to usurp the thrown in the last chapter, comes to Bathsheba's house. He reminds her that the throne was rightfully his, and asks her one favour, which is to get Solomon to grant him Abishag, David's uh, naked virgin 'nurse.' For some incredibly stupid reason that isn't given, Bathsheba agrees.
She goes to Solomon and says she has a request and gets him to promise to grant it before she tells him what it is, proving the apple hit every branch of the stupid tree on its way down. He wonders why she would betray him like this, and suggests she also promise Abithar the kingdom, then vows to kill Abiathar as well. That's a lot of murders for one chapter.
Solomon sends his assassin Benaiah along to kill Adonijah, who dispatches him handily. He also banishes Abiathar the priest. Joab senses the danger in the air and flees to the temple, where he, too, grabs onto the horns of the altar. Solomon is clearly less concerned with the sacredness of holy objects than David, because he sends Benaiah after him. Benaiah demands that Joab come out, but Joab refuses. So Benaiah goes back to Solomon and tells him he won't come out. So Solomon tells him to kill him in the temple. After all, there's so much blood in there, nobody would know if it was just sacrifices from all the people who had sex that day or from a human who sought sanctuary for his life.
Benaiah is rewarded with a cushy room in Solomon's palace, and a new priest is installed as well.
Solomon is finally ready for his third revenge killing. He summons Shimei and orders him to move to Jerusalem. He then tells him that if he leaves, he'll be killed. Shimei manages to remember not to leave for three years, but he's no smarter than any of the others, so when his servants run away, he goes to Gath to retrieve them, and Benaiah is sent once again to assassinate someone.