Acts 1:2
Identity
The Holy Spirit will now be the identity who moves through the earth and everyone who comes in contact with him is trying to figure out who he is and who they are relative to him. Now he is the Jesus identity fully present. This is the handoff.
Giving instructions through the Holy Spirit
If Jesus is with them and showing them convincing proofs he is alive, why is the Holy Spirit mentioned here as the agent of instruction? Isn't Jesus himself instructing them? Is this a combination of Jesus speaking and the Spirit affirming in their hearts? This is a very curious statement. Couple this with Jesus' command for them to wait on the Holy Spirit and it becomes even more curious. The Spirit is present and active but not fully present and active or as present and active as He will be when Pentecost comes. This brief period of time must be like a turnover of command on a ship. Both captains are present at once but the outgoing is giving power and authority to the incoming.
What could be the reason(s) for this? Perhaps it is so the disciples are ready to recognize the Spirit when he comes. They are getting both voices at one time and can hear that Jesus and the Spirit speak the same language - have one voice. Maybe this is the burning experienced by the disciples on the way to Emmaus when Jesus was opening the Scriptures to them.
Was this "turnover" of command a new way of being led by Jesus who had only followed the Father's leading before the resurrection? Now the Spirit is leading the risen Jesus and so he is experiencing what his followers must experience after he leaves. This would complete his identification with us who will be led through the Holy Spirit and he will completely understand what it is like to be a Christian dependent upon the Comforter.
Acts 1:3
Kingdom
After 30+ years and a brutal separation from God the Father, Jesus the Son is not in a hurry to get home. This is counterintuitive. The work is done - he said so himself on the cross (John 19:30). Why 40 days more? Whatever it is you'd think it must be pretty important to delay his return to heaven. But we do not get the inside story on Jesus's 40 day seminar. We only get the table of contents as it were. He proves his identity beyond their doubts and he teaches about the kingdom.
What can we make of this? Knowing that Jesus is alive is essential - He offers many convincing proofs. Knowing about a new administration is essential - it is the only subject Jesus teaches.
What we know is that Jesus is alive and a new kingdom is either in place or coming or both. This must lead to the conclusion that Jesus's command for his followers to wait upon the Holy Spirit must have something to do with both his revealed, resurrection-type life and the kingdom. Holy Spirit is the kingdom come not just as an administrator of life like human kings but as the indestructible life that enters the heart of believers and sets up an internal administration. A life like Jesus's life.