It is interesting for me to think about the intercessory role of Christ. Immediately we begin to talk about Christ's intercessory role, we must split that work of intercession into two distinct phases. There is Christ the intercessor on earth and there is the continual intercession that Christ makes on our behalf before the Father.
Both flow from the priestly office of Christ. The former is contained within Christ's work on earth during the incarnation and culminates in his the offering up of
himself as a sacrifice for us. The latter refers to his making continual intercession for us before the Father after his ascension.
When on earth Jesus interceded for people, as can be seen in Luke 23:34 (where Jesus prays for those who crucified him), John 17: 20 (where Jesus prays for those who will believe in him through the witness of the disciples) and Heb 5:7 (" During the days of Jesus’ life on earth, he offered up prayers and petitions with fervent cries and tears to the one who could save him from death, and he was heard because of his reverent submission").
Since his ascension, Jesus' intercessory role has changed. Still flowing from his office as our Great High Priest, Jesus now exercises this function in heaven, where
he is said to appear in the presence of God for us as the writer to the Hebrews says in Heb 9: 12 and 24: ("12 He did not enter by means of the blood of goats and calves; but he entered the Most Holy Place once for all by his own blood, thus obtaining eternal redemption ... 24 For Christ did not enter a sanctuary made with human hands that was only a copy of the true one; he entered heaven itself, now to appear for us in God’s presence").
Jesus now stands before the Father representing us on the basis of his own
once-for-all-perfect sacrifice. Thus he pleads for and obtains the fulfillment of all the
promises of the everlasting covenant according to 1 John 2:1 ("My dear children, I write this to you so that you will not sin. But if anybody does sin, we have an advocate with the Father—Jesus Christ, the Righteous One"), John 17:24 (“Father, I want those you have given me to be with me where I am, and to see my glory, the glory you have given me because you loved me before the creation of the world.") and Heb 7:25 ("Therefore he is able to save completely those who come to God through him, because he always lives to intercede for them.").
He is moved with compassion when we are hurt and he feels the pain of our struggle with temptation here on earth because he is both a merciful and a faithful high priest: Heb 2:17 - 18 ("For this reason he had to be made like them, fully human in every way, in order that he might become a merciful and faithful high priest in service to God, and that he might make atonement for the sins of the people. 18 Because he himself suffered when he was tempted, he is able to help those who are being tempted.") and Heb 4: 15 - 16: ("For we do not have a high priest who is unable to empathize with our weaknesses, but we have one who has been tempted in every way, just as we are —yet he did not sin. 16 Let us then approach God’s throne of grace with confidence, so that we may receive mercy and find grace to help us in our time of need"). This intercession is an essential part of his
work as the one mediator between God and human beings. It is through Christ that we have "access" to the Father according to John 14:16, Eph 2: 18 and 3:12.