I want to think a little about Christ as mediator in the New Testament, seeing how far I can get with the basic rubric of prophet, priest, and king.
Christ as Prophet and Word of God
Luke 4:16-21 understands Jesus' earthly mission in prophetic terms. The Gospel of Luke presents Isaiah 61:1-2 as the appropriate interpretive lens through which to view Jesus' mission. The Spirit of the Lord anointed Jesus to mediate and proclaim good news to the poor, liberty to captives, and sight to the blind. Jesus likely referred to himself as a prophet on more than one occasion (e.g., Matt. 13:57; Luke 13:33), and others also seem to have understood him in this way (e.g., Matt. 21:11; Mark 6:15).
The book of Acts understood Jesus to be the prophet like Moses predicted in Deuteronomy 18:15 (3:22; 7:37), and the Gospel of John alludes to this passage in more than one instance in relation to Christ (John 1:21, 25; 6:14; 7:40). God's statement at the Transfiguration that the disciples were to "Listen" to Jesus (Mark 9:7) draws on the same verse in Deuteronomy. Jesus' role as a prophet in these passages seems not so much about specific prophecies that he uttered on earth. Rather, Jesus' prophetic "word" here seems more directly related to the more abstract "word of salvation" proclaimed through his incarnation (cf. John 6:14), death, and resurrection (cf. Heb. 2:3). Jesus as prophet is the "apostle" of our confession (Heb. 3:1) whom God sent as a mediator to reconcile the world to himself (cf. 2 Cor. 5:18).
We can thus speak of Jesus' prophetic mediation on two levels. On one level, Jesus functioned in Galilee as a prophet who brought on God's behalf both good news to the "lost sheep of Israel" and warnings of coming judgment. The miracles he performs echo those of Elijah and Elisha, and his symbolic acts find their meaning against the backdrop of the words of prophets like Jeremiah (e.g., Jer. 7:11). On another level, Christ's cosmic ministry brokers a new covenant with all humanity, as Moses brokered the first covenant with Israel. Early Christians likely conceptualized such mediation through the lens of patron-client relationships, with Christ as the designated broker of God's grace.
John 1:17 gives one perspective on these two mediations: "The law indeed was given through Moses; grace and truth came through Jesus Christ." The idea that Christ brokered God's gracious patronage to both Jew and Gentile is a key concept for Paul's writings. The "law brings wrath" (Rom. 4:15) "since all have sinned" (Rom. 3:23). Salvation, escape from God's wrath, is a gift of God (cf. Eph. 2:8) that follows from God's willingness to justify the ungodly on the basis of their faith (Rom. 4:5). Justification thus "depends on faith, in order that the promise may rest on grace" (Rom. 4:16).
For Paul, such grace can no longer come directly, as it apparently did in the case of Abraham, who "believed God, and it was reckoned to him as righteousness" (Rom. 4:3; Gen. 15:6). God has rather brokered this new covenant through Jesus Christ. Several New Testament writers emphasize the exclusivity of this path to God: "There is salvation in no one else, for there is no other name under heaven given among mortals by which we must be saved" (Acts 4:12), and "I am the way, and the truth, and the life. No one comes to the Father except through me" (John 14:6). Salvation is possible now because of the consummate mediatorial act Paul describes as the faith of Jesus Christ (Rom. 3:22; Gal. 2:16), his obedience "to the point of death" (Phil. 2:8). Only "by the one man's obedience the many will be made righteous" (Rom. 5:19). The New Testament thus seems not only to understand Christ as a broker of God's grace, but indeed the only truly effective broker.
Paul presents the cosmic scope of this mediation through the image of Christ as the "last Adam." "[S]in came into the world through one man," Adam, "and death came through sin" (Rom. 5:12). By contrast, with Christ, "one man's act of righteousness leads to justification and life for all" (Rom. 5:18). "The first man, Adam, became a living being" but "the last Adam became a life-giving spirit" (1 Cor. 15:45). Indeed, the exalted Christ has brokered a new covenant in which the Spirit of Christ inhabits the renewed children of God (cf. Rom. 8:9, 14; 2 Cor. 3:6).
Christ is thus a prophetic mediator well beyond the bounds of any Old Testament prophet, including Moses. "Long ago God spoke to our ancestors in many and various ways by the prophets, but in these last days he has spoken to us by a Son" (Heb. 1:1-2). This prophetic logos is the very Word of God itself. The Gospel of John draws on the Middle Platonic idea of God's logos and applies it to Jesus as the very will and purpose of God for the world. For this reason the New Testament can speak of Christ as the instrument of God in creation, the one "through whom he also created the worlds" (Heb. 1:2; cf. John 1:3; 1 Cor. 8:6; Col. 1:16).
From one point of view, Christ is thus God's highest ambassador to the world. "God so loved the world that he gave his only Son, so that everyone who believes in him may not perish but may have eternal life" (John 3:16). Christ is God's consummate apostle (Heb. 3:1), sent with the commission to bring salvation to all who believe. He is the very Word of God (John 1:1) who is one with the Father (e.g., John 10:30; 17:11). He is the ultimate prophet, through whom God has proclaimed and effected reconciliation with the world (2 Cor. 5:19).