“By the hand of my servant David.” There is no place in Scripture where this prophecy and promise was specifically stated, but the fact that the elders did not challenge it and agreed to follow David means that in essence, it was well known.
“out of the hand of the Philistines.” There are likely many things that Abner said when he met with the elders of Israel, but it is clear from what is in Scripture that he spoke in terms of their interests and what they wanted, and they certainly wanted to be delivered from the threat of the Philistines, which David did when he became king.