The Holy One will not see decay
David's confidence that the Holy One will not see decay — Peter reads it of the resurrection, while Acts itself notes that David died and was buried (Acts 2:29).
Psalm 16:8-11
8I have set Yahweh always before me. Because he is at my right hand, I shall not be moved.
9Therefore my heart is glad, and my tongue rejoices. My body shall also dwell in safety.
10For you will not leave my soul in Sheol, neither will you allow your holy one to see corruption.
11You will show me the path of life. In your presence is fullness of joy. In your right hand there are pleasures forever more.
Acts 2:25-32
25For David says concerning him, ‘I saw the Lord always before my face, for he is on my right hand, that I should not be moved.
26Therefore my heart was glad, and my tongue rejoiced. Moreover my flesh also will dwell in hope;
27because you will not leave my soul in Hades, neither will you allow your Holy One to see decay.
28You made known to me the ways of life. You will make me full of gladness with your presence.’
29“Brothers, I may tell you freely of the patriarch David, that he both died and was buried, and his tomb is with us to this day.
30Therefore, being a prophet, and knowing that God had sworn with an oath to him that of the fruit of his body, according to the flesh, he would raise up the Christ to sit on his throne,
31he foreseeing this spoke about the resurrection of the Christ, that his soul wasn’t left in Hades, and his flesh didn’t see decay.
32This Jesus God raised up, to which we all are witnesses.
What each tradition says
Rabbinic / Midrashic
Midrash Tehillim reads Psalm 16:10’s “pious one” as the Holy One, citing Jeremiah 3:12, while noting David also called himself “pious” in Psalm 86:2. Rabbi Alexandri says anyone who hears his disgrace and remains silent is called pious; David did so and was therefore called pious.
Midrash Tehillim (the Midrash on Psalms), ch. 16, §8; Sefaria Community Translation, Midrash Tehillim (Sefaria Community Translation, CC0), via the Sefaria API — ch. 16, on Psalm 16:10
Patristic
Augustine says the flesh will rest in hope, not fail to destruction but sleep in hope of the resurrection. God will not leave the soul in hell or give it as a possession to those below. Nor will He allow the sanctified body, whereby others are also to be sanctified, to see corruption.
Augustine of Hippo (354-430), Expositions on the Book of Psalms, in Nicene and Post-Nicene Fathers, ser. 1, vol. 8 (ed. Philip Schaff; New York: Christian Literature Publishing Co., 1888) — Exposition of Psalm 16, §9-10
Catholic
Maas holds that Christ's Resurrection is necessarily glorious: it means not only the reunion of body and soul but also the glorification of the body. Christ's body was to know no corruption, yet rose soon after death, once enough time had passed to leave no doubt that He had truly died.
Anthony J. Maas (1859-1927), The Catholic Encyclopedia, s.v. 'Resurrection of Jesus Christ' (New York: Robert Appleton Company, 1911) — section 'Character of Christ's resurrection'
Orthodox
Chrysostom observes that before their thoughts can enter at all into his meaning, he brings David upon them as an authority that sets aside all human reasoning. He cites David as saying, with reference to Him. Chrysostom notes that the testimony is lowly, so he begins the citation further up with matters of lowlier import.
John Chrysostom (c. 349-407), Homilies on the Acts of the Apostles, in Nicene and Post-Nicene Fathers, ser. 1, vol. 11 (ed. Philip Schaff; T&T Clark, Edinburgh, 1889) — Homily VI, on Acts 2:25-31
Reformed / Protestant
Calvin says Peter justly concludes that David could not have gloried in this way except by the spirit of prophecy. David must have had a special regard for the Author of life, who was promised to him. Only that one was to be honored with this privilege in its fullest sense.
John Calvin (1509-1564), Commentary on the Book of Psalms, vol. 1 (trans. James Anderson; Edinburgh: Calvin Translation Society, 1845) — commentary on Psalm 16:10
Evangelical
Wesley reads “hell” as the state of the dead, and “Holy One” as Christ, God’s holy Son whom he sanctified and sent into the world; being called the holy one of God is peculiar to Christ. “To see” means to be corrupted or putrefied in the grave, as other bodies are.
John Wesley (1703-1791), Explanatory Notes upon the Old Testament (1765), in Wesley's Notes on the Bible (CCEL) — note on Psalm 16:10