For the rest of 1 Samuel, Saul continues to be king. Throughout, David is being prepared for leadership, often through some very difficult challenges. Many of those challenges come from Saul who tries to kill David to prevent him from becoming king. Despite Saul’s mistreatment of him, David grieves when he learns of the death of Saul and his son Jonathan.
David respected the office of king of Israel and realized God had put Saul in that place. Paul tells us to do the same thing in Romans 13:1. The news media love to point out the weaknesses and mistakes of our government leaders. It’s easy to become disrespectful toward those in authority, but God says He has put them in place to be obeyed. David understood this even when his life was directly threatened.