While there are a few Psalms and other places in Scripture dealing with their relationship, the most prominent place to observe the relationship between these two men is 1 Samuel 15-31. The reader can see a definite shift in the narrative between 1 Samuel 15 and 16. Saul is rejected by the LORD in one chapter and the boy David is anointed by the Lord as the king to take his place. The readers of 1 Samuel are given clues to the rejection of Saul and the rise of David, but as the story played out in real-time it would have likely been far more jolting to David.
Then a shoot will grow from the stump of Jesse, and a branch from his roots will bear fruit. The Spirit of the Lord...
And when the thousand years are ended, Satan will be released from his prison and will come out to deceive the nations that are...
Let not mercy and truth forsake you. Bind them around your neck. Write them on the tablet of your heart and so find favor...