Tehillim 22, which starts as “A Song of David,” deals with events that were destined to happen hundreds of years after King David’s time. David foresaw, with prophecy, the Babylonian/Persian exiles and the threat of Achashverosh and Haman over the Jewish people. Alshich, the commentator, says that King David dedicated a psalm to Esther because he had a hand in her personal salvation by not immediately killing Shimi ben Gera when he rebelled against David. Both Mordechai and Esther were to be descendants of Shimi ben Gera. Being that the nation of Israel would need salvation, David would forgo his dignity to save his people. This psalm is in honor of the Purim miracle.
The Vilna Gaon would recite Psalm 22 as the Shir Shel Yom on Purim day.