'Established' in the Bible

Solomon then assumed his father David's throne, and his kingdom was firmly established.

Now therefore, as the LORD lives, who has established me and set me on the throne of my father David, and who has established a dynasty, just like he promised, Adonijah will surely be executed today."

But King Solomon will be blessed, and David's throne will be established in the presence of the LORD forever."

So the king gave orders to Jehoiada's son Benaiah to go out, attack Shimei, and kill him. That is how the kingdom was established under Solomon's control.

Nevertheless, for the sake of David, the LORD his God maintained a lamp for David in Jerusalem by raising up his son after him so that Jerusalem would be established,

As soon as he was established as king, he killed everyone in the household of Jeroboam. He left not even one single person alive. He destroyed them completely, just as the LORD had spoken through his servant Ahijah the Shilonite,