This is clearly a reference to the Holy Spirit. With his outpouring on Pentecost, the third person of the Trinity has his home on earth (John 14:23, John 14:26). Through this Spirit, Christ Jesus speaks to the churches (Revelation 2:7, Revelation 2:11, Revelation 2:17, etc.). In the present passage the Spirit responds to Jesus’ promise to return to Earth with his own eager appeal to the second person: Come!
17 The Spirit and the Bride say, “Come.” And let the one who hears say, “Come.” And let the one who is thirsty come; let the one who desires take the water of life without price.