Bathsheba came to King David, told him that Adonijah had proclaimed himself king, and pointed out to David that he had promised her that Solomon would succeed him as king. Then David told her that, indeed, Solomon would be king. Bowing and kneeling before the king, Bathsheba said, "May my lord King David live forever!"

I believe that, in fact, King David will live forever, once he is resurrected at the end of the age. I also believe that he will be the king of Israel again, with Jesus reigning as King of the World. All of this is explained here:

http://www.tedmontgomery.com/bblovrvw/C_13b.html#David_the_king