Baptism is the obvious connection between the beginning of Jesus’ ministry in Matthew 3 and its conclusion in Matthew 28.
In Matthew 3:11, John the Baptist announced that he baptized in water, but one would come after him who would baptize with the Holy Spirit. Then, in Matthew 3:13-17, John baptized Jesus in the Jordan, after which the Spirit of God descended on Jesus in the form of a dove .
In Matthew 28:19, the risen Jesus told the eleven disciples to baptize people all nations (i.e. including Gentiles) into the name of the Father, Son and Holy Spirit, teaching them to observe everything he had taught them.
The baptism scene and the resurrection appearance are Matthew’s only two references to baptism, and they form literary bookends in the gospel story. This literary device is known as an inclusio. These scenes also contain two of Matthew’s minimal references to the Holy Spirit. The phrase “Holy Spirit” otherwise makes few appearances in Matthew’s gospel.
I conclude, then, that Matthew envisions the church – the world-wide assembly of faithful disciples, who are united to the triune God in baptism, and who live in accordance with Jesus’ teachings as they await his return – to be the fulfillment of John’s Holy Spirit prophecy.