David sang that God would not abandon His Holy One to the grave. At Pentecost, Peter pointed at an empty tomb and said David was talking about Jesus.
The Shadow
Psalm 16 is a song of strange confidence. David sets the Lord always before him, and then says something no one standing at a graveside has any right to say: my flesh also will rest in hope. For You will not leave my soul in Sheol, nor will You allow Your Holy One to see corruption. You will show me the path of life.
Here is the problem, and everyone in Jerusalem knew it. David died. He was buried, and his tomb sat in the city for a thousand years where anyone could visit it. His flesh saw corruption the way all flesh does. So either the psalm promised more than it delivered, or David was singing about someone else.
The Fulfillment
That is exactly the argument Peter makes in the first Christian sermon ever preached. At Pentecost, with the city still buzzing about an empty tomb, Peter quotes this psalm and then points at the hole in it: David is dead and buried, and his tomb is with us to this day. So David, being a prophet, was foreseeing the resurrection of the Christ, that His soul was not left in Hades, nor did His flesh see corruption. Paul preaches the same psalm the same way in Acts 13. The apostles' first case for the resurrection was not only that the tomb was empty; it was that Scripture had required it to be. The Holy One could not rot. The path of life ran straight through a grave and out the other side.
Death did not interrupt the psalm. Death was the route the psalm had promised to survive.
Him All Along
Notice where the psalm lands: in Your presence is fullness of joy. Not in your performance. Not in your progress. Presence. Because the Holy One was not abandoned to the grave, you will not be either — the rest of hope David sang about is now simply yours. The path of life has already been walked, and it ends at the right hand of God, where your Savior is seated and your future is kept.