“For David, after he had served his own generation by the will of God, fell on sleep.”- Act 13:36

It is remarkable that David should say, in the sixteenth Psalm, “Thou wilt not leave my soul in hell; neither wilt thou suffer thine Holy One to see corruption,” and yet that Paul should say concerning him, when preaching at Antioch, that he “saw corruption.” The key to this apparent contradiction is the fact that David did not speak of himself, but of his Lord. Peter, in his memorable sermon on the day of Pentecost, quotes the words of the psalmist, applies them to his risen Redeemer, and distinctly affirms that, in the Psalm, “David speaketh concerning Him.”

It is worthy of notice that Peter and Paul both use the same argument about this statement of David. These two apostles did not always agree; but however much they might differ about other matters, they were of one mind about the resurrection of Christ. I hope that whatever differences there may be among true preachers of the gospel, they will always be one in declaring the resurrection of our Lord. This corner-stone of the gospel must never be displaced or dishonoured. The good news we are commissioned to declare is the same that Paul received and delivered, “that Christ died for our sins according to the Scriptures; and that He was buried, and that He rose again the third day according to the Scriptures.” Chief among the Scriptures fulfilled by the resurrection of Christ stands this word, which David, inspired by the Holy Ghost, wrote so long before the event: “Thou wilt not leave my soul in hell; neither wilt thou suffer thine Holy One to see corruption.” The resurrection of Christ is the top-stone of our faith. Because “He, whom God raised again, saw no corruption,” Paul was able to say this to his hearers, “Be it known unto you therefore, men and brethren, that through this man is preached unto you the forgiveness of sins: and by Him all that before are justified from all things, from which ye could not be justified by the law of Moses.” ~ C.H. Spurgeon

https://www.blueletterbible.org/comm/spurgeon_charles/sermons/2243.cfm