In prophetically speaking, God is glorifying himself through the declaration (the speaking) of the gospel of Jesus Christ by the power of the Holy Spirit. The Triune God is preaching the cross and he does so for his own glory. More than this, the Father is rewarding the Son with a trophy for the work he will accomplish. And that trophy is a people called by his name.
In John 17 Jesus prays his high priestly prayer, a beautiful picture of the interaction between the Father and the Son and the eternal love that they have always had for each other; a sacrificial, selfless love, now about to be on full display to the creation as Jesus goes to the cross. Both the Father and the Son are glorifying the other through the work of the cross.
17 When Jesus had spoken these words, he lifted up his eyes to heaven, and said, “Father, the hour has come; glorify your Son that the Son may glorify you, 2 since you have given him authority over all flesh, to give eternal life to all whom you have given him. 3 And this is eternal life, that they know you, the only true God, and Jesus Christ whom you have sent. 4 I glorified you on earth, having accomplished the work that you gave me to do. 5 And now, Father, glorify me in your own presence with the glory that I had with you before the world existed. – John 17:1-5
And not to be left out, just before this, in John 16 Jesus explained to his disciples that the Holy Spirit would glorify him soon and through the act of speaking:
13 When the Spirit of truth comes, he will guide you into all the truth, for he will not speak on his own authority, but whatever he hears he will speak, and he will declare to you the things that are to come. 14 He will glorify me, for he will take what is mine and declare it to you. 15 All that the Father has is mine; therefore I said that he will take what is mine and declare it to you. – John 16:13-15
Back again in John 17 in Jesus’ high priestly prayer we see him explain that the glory the Father, Son and Spirit have always shared will now be shared with a people so that these people may glorify God being united as one, just as our Triune God is one.
20 “I do not ask for these only, but also for those who will believe in me through their word, – John 17:20
22 The glory that you have given me I have given to them, that they may be one even as we are one, 23 I in them and you in me, that they may become perfectly one, so that the world may know that you sent me and loved them even as you loved me. 24 Father, I desire that they also, whom you have given me, may be with me where I am, to see my glory that you have given me because you loved me before the foundation of the world. – John 17:22-24
And it is in Christ that they shall be united and perfected, in the bond of selfless, sacrificial love; the love of God in the cross of Christ. All of this done to the glory of God by his prophetic speaking.
13 By this we know that we abide in him and he in us, because he has given us of his Spirit. 14 And we have seen and testify that the Father has sent his Son to be the Savior of the world. 15 Whoever confesses that Jesus is the Son of God, God abides in him, and he in God. 16 So we have come to know and to believe the love that God has for us. God is love, and whoever abides in love abides in God, and God abides in him. 17 By this is love perfected with us, so that we may have confidence for the day of judgment, because as he is so also are we in this world. 18 There is no fear in love, but perfect love casts out fear. For fear has to do with punishment, and whoever fears has not been perfected in love. 19 We love because he first loved us.. – 1 John 4:13-19
The Father is giving his Son a people, the elect, as a reward. A people that will glorify God as they share in his perfect love by prophetically hearing and declaring the gospel of Jesus Christ.