Our great high priest
Christ's high-priestly works of sacrifice and intercession satisfy God's justice for sin.
God's justice demands a penalty for every breach of his Law; this must be so for God cannot look upon sin with favour. His Being and his moral government of the created order insist upon the penalty; and the penalty is death. "Without the shedding of blood there is no remission." Since it was impossible for man to redeem himself, God in his grace intervened to emancipate him from condemnation and death by ordaining His own Son as high-priest, i.e., to represent the people (sinful as they are) before him. Christ accomplished this by taking upon himself the penalty, as a substitute. This he did voluntarily, so there was no injustice involved.
Now that Christ is at the Father's right hand, exalted in heaven, he is ever living to make intercession for his redeemed. His very presence, as the Lamb that was slain, but now lives for ever and ever, guarantees that no accusation might be brought forward against the elect. For the penalty was paid once for all, and is efficacious. He is therefore both faithful and just to forgive: faithful because of his promise, and just because forgiveness is merited for His own because of Calvary.
Christ's high-priestly works of sacrifice and intercession bring His people back to God.
The sacrifice of Christ is definitely reconciliatory: whereas before we were enemies of God though wicked works, now Christ has wrought an atonement. As Mediator (for this is what a priest basically is) he brings man back to God.
And this friendship with God is brought to pass in the believer's experience as Christ continues his ministry of intercession, applying the merits of his work by the heaven-sent Holy Spirit, who performs the new birth in sinners' hearts and subsequently sanctifies them and changes them all the more into the image of Christ.