Hebrews 3:1 encourages us  to consider Jesus.  It goes on to say two things about our Lord.

1.) Apostle: representing God before men
2.) High Priest: representing men before God

J.I. Packer lays out beautifully, per usual, the glory of Jesus as our mediator:

MEDIATION

JESUS CHRIST IS THE MEDIATOR BETWEEN GOD AND MAN

For there is one God and one mediator between God and men, the man Christ Jesus. 1 TIMOTHY 2:5

The saving ministry of Jesus Christ is summed up in the statement that he is the “mediator between God and men” (1 Tim. 2:5). A mediator is a go-between who brings together parties who are not in communication and who may be alienated, estranged, and at war with each other. The mediator must have links with both sides in order to identify with and maintain the interests of both and represent each to the other on a basis of good will. Thus Moses was mediator between God and Israel (Gal. 3:19), speaking to Israel on God’s behalf when God gave the law (Exod. 20:18-21) and speaking to God on Israel’s behalf when Israel had sinned (Exod. 32:9-33:17).

Every member of our fallen and rebellious race is by nature “hostile to God” (Rom. 8:7) and stands under God’s wrath (i.e., the punitive rejection whereby as Judge he expresses active anger at our sins, Rom. 1:18; 2:5-9; 3:5-6). Reconciliation of the warring parties is needed, but this can occur only if God’s wrath is somehow absorbed and quenched and man’s anti-God heart, which motivates his anti-God life, is somehow changed. In mercy, God the angry Judge sent his Son into the world to bring about the needed reconciliation. It was not that the kindly Son acted to placate his harsh Father; the initiative was the Father’s own. In Calvin’s words, “in an inconceivable way he loved us even when he hated us,” and his gift to us of the Son as our sin bearer was the fruit of that love (John 3:14-16; Rom. 5:5-8; 1 John 4:8-10). In all his mediatorial ministry the Son was doing his Father’s will.

Objectively and once for all, Christ achieved reconciliation for us through penal substitution. On the cross he took our place, carried our identity as it were, bore the curse due to us (Gal. 3:13), and by his sacrificial blood-shedding made peace for us (Eph. 2:16; Col. 1:20). Peace here means an end to hostility, guilt, and exposure to the retributive punishment that was otherwise unavoidable—in other words, pardon for all the past and permanent personal acceptance for the future. Those who have received reconciliation through faith in Christ are justified and have peace with God (Rom. 5:1, 10). The mediator’s present work, which he carries forward through human messengers, is to persuade those for whom he achieved reconciliation actually to receive it (John 12:32; Rom. 15:18; 2 Cor. 5:18-21; Eph. 2:17).

Jesus is “the mediator of a new covenant” (Heb. 9:15; 12:24)—that is, the initiator of a new relationship of conscious peace with God, going beyond what the less effective Old Testament arrangements for dealing with the guilt of sin could ever secure (Heb. 9:11-10:18).

One of Calvin’s great contributions to Christian understanding was his observation that the New Testament writers expound Jesus’ mediatorial ministry in terms of the threefold office (“office” means set task, or defined role) of prophet, priest, and king.

The three aspects of Christ’s work are found together in the letter to the Hebrews, where Jesus is both the messianic king, exalted to his throne (1:3, 13; 4:16; 2:9), and also the great High Priest (2:17; 4:14-5:10; chs. 7-10), who offered himself to God as a sacrifice for our sins. In addition, Christ is the messenger (“apostle,” the one sent to announce, 3:1) through whom the message of which he is himself the substance was first spoken (2:3). In Acts 3:22 Jesus is called a prophet for the same reason that Hebrews calls him an apostle, namely, because he instructed people by declaring to them the Word of God.

While in the Old Testament the mediating roles of prophet, priest, and king were fulfilled by separate individuals, all three offices now coalesce in the one person of Jesus. It is his glory, given him by the Father, to be in this way the all-sufficient Savior. We who believe are called to understand this and to show ourselves his people by obeying him as our king, trusting him as our priest, and learning from him as our prophet and teacher. To center on Jesus Christ in this way is the hallmark of authentic Christianity.