Look at the second chapter of Acts. See something that is often overlooked. Whenever Jesus is honored and exalted, the Holy Spirit comes. Contrary to what some people assume, the important thing here was not that the Holy Spirit had come. More importantly, the Holy Spirit came to confirm the message of the Lord Jesus Christ. Thousands were saved through the gospel and the power of the Holy Spirit.
On the Day of Pentecost, the Holy Spirit exalted the risen Christ. The great outpouring of the Holy Spirit was the work of the living Christ. Pentecost declared Jesus is risen indeed! The Holy Spirit always works to exalt the Lord Jesus Christ. Come Holy Spirit to save people through the gospel of Jesus Christ.
Jesus promised those early disciples that He would empower them with the Holy Spirit to witness for Him (Acts 1:8). That's exactly what happened on the Day of Pentecost. They witnessed the work of the Holy Spirit drawing people to Christ from many different nations.
The Holy Spirit came to exalt Jesus on the Day of Pentecost through preaching. The apostle Peter preached a sermon about Christ from the Old Testament Scripture and declared the resurrection of Jesus from the dead. The Holy Spirit was the witness to the truth of Jesus Christ. On the Day of Pentecost, Jesus Christ was exalted in the outpouring of the Holy Spirit. Come Holy Spirit, as we declare Jesus is Lord.