Albert Barnes Commentary 1 Samuel 16:21

"And David came to Saul, and stood before him: and he loved him greatly; and he became his armorbearer." — 1 Samuel 16:21 (ASV)

The difficulty of reconciling this verse with 1 Samuel 17:55–58 can be explained in this way: The words here describe what ultimately resulted from David’s first visit to Saul and his skill in music, which is why they are placed here. However, these events did not actually happen until after David’s victory over Goliath (see 1 Samuel 18:2).

It is quite conceivable that if David had only played once or twice for Saul and then returned to his father’s house for some months, Saul might not have recognized him.