The entire mission of the Son and the Holy Spirit, in the fullness of time, is contained in this: that the Son is the one anointed by the Father’s Spirit since his Incarnation – Jesus is the Christ, the Messiah.
Everything in the second chapter of the Creed is to be read in this light. Christ’s whole work is in fact a joint mission of the Son and the Holy Spirit. Here, we shall mention only what has to do with Jesus’ promise of the Holy Spirit and the gift of him by the glorified Lord.
Jesus does not reveal the Holy Spirit fully, until he himself has been glorified through his Death and Resurrection. Nevertheless, little by little he alludes to him even in his teaching of the multitudes, as when he reveals that his own flesh will be food for the life of the world. He also alludes to the Spirit in speaking to Nicodemus, to the Samaritan woman, and to those who take part in the feast of Tabernacles. To his disciples he speaks openly of the Spirit in connection with prayer and with the witness they will have to bear.
Only when the hour has arrived for his glorification does Jesus promise the coming of the Holy Spirit, since his Death and Resurrection will fulfill the promise made to the fathers. The Spirit of truth, the other Paraclete, will be given by the Father in answer to Jesus’ prayer; he will be sent by the Father in Jesus’ name; and Jesus will send him from the Father’s side, since he comes from the Father. the Holy Spirit will come and we shall know him; he will be with us for ever; he will remain with us. the Spirit will teach us everything, remind us of all that Christ said to us and bear witness to him. the Holy Spirit will lead us into all truth and will glorify Christ. He will prove the world wrong about sin, righteousness, and judgment.
At last Jesus’ hour arrives: he commends his spirit into the Father’s hands at the very moment when by his death he conquers death, so that, “raised from the dead by the glory of the Father,” he might immediately give the Holy Spirit by “breathing” on his disciples. From this hour onward, the mission of Christ and the Spirit becomes the mission of the Church: “As the Father has sent me, even so I send you.”
From the Catechism of the Catholic Church 727-730