Evidently David had received a special revelation from the Lord that he would not die then, but would escape from whatever distress he was enduring (cf. Psalm 16:7 a). The phrase "my glory rejoices" (NASB) means David rejoiced that his glory as a living person blessed by God would continue to be a source of joy for him. God would spare his life. Of course, David did not mean he would live forever, by bypassing death. He only meant that he would not die then. David was God"s "holy one" ( Psalm 16:10) in that God had set him apart for a special purpose and because his life was indeed God"s, as he described earlier in this psalm. [1][source]
The Apostle Paul referred to Psalm 16:10 as a messianic prophecy of Jesus Christ"s resurrection ( Acts 13:35). This is one of the few clear references to resurrection in the Old Testament (cf. Isaiah 26:19; Daniel 12:2). [2][source]
"The16th Psalm is a prediction of the resurrection of the King. As a prophet, David declared that, not at His first advent but at some time subsequent to His death and resurrection, the Messiah would assume the Davidic throne. Cp. Acts 2:25-31 with Luke 1:32-33 and Acts 15:13-17." [3][source]