THE COMING OF THE HOLY SPIRIT, the "Counselor" or Paraclete, is dependent on Jesus' "going away," i.e., his death by crucifixion, subsequent resurrection, and exaltation (John 16:7; cf. 7:37-39).
This raises important questions about the relationship between the Spirit's role under the old covenant, before the cross, and his role this side of it. That is worthy of careful probing. Here, however, John's emphasis on the Spirit's work must be made clear.
At the end of John 15, the Counselor, we are told, will bear witness to Jesus, and to this task to which the disciples of Jesus will lend their voices (15:26-27). The prime witness falls to the Spirit. In John 16:8-11, the Counselor convicts the world of sin, righteousness, and judgment. He does so because Jesus is returning to the Father and no longer exercises the role of convicting people himself.
If the Holy Spirit bears witness to Jesus in 16:8-11, in 16:12-15 he brings glory to Jesus by unpacking Christ to those who attended the Last Supper (the "you" in v. 12 cannot easily be taken in any other way, and controls the other instances of "you" in the rest of the paragraph; cf. also 14:26). As Jesus is not independent of his Father, but speaks only what the Father gives him to say (5:16-30), so the Spirit is not independent of the Father and the Son: "He will not speak on his own; he will speak only what he hears" (16:13). His focus is Jesus: "He will bring glory to me by taking from what is mine and making it known to you" (16:14). And of course, even here what belongs to Jesus comes from the Father: "All that belongs to the Father is mine. That is why I said the Spirit will take from what is mine and make it known to you" (16:15).
The reason why Jesus himself has not unpacked everything about himself and his mission to the disciples is that they are not yet ready to bear it (16:12). Even this late in their discipleship, they cannot quite integrate in their own minds the notion of a King-Messiah and the notion of a Suffering Messiah. Until that point is firmly nailed down, the way they read their Scriptures — what we call the Old Testament — will be so skewed by political and royal aspirations that they are not going to get it right.
How much of the Spirit's work focuses on Jesus Christ — bearing witness to him, continuing certain aspects of his ministry, unpacking his significance!
Exodus 37; John 16; Proverbs 13; Ephesians 6