Is Jesus Christ our great high priest?
Yes. Because Jesus lives forever, he has a permanent priesthood. Therefore, he is able to save completely those who come to God through him, because he always lives to intercede for them.
Catechism for the Global Methodist Church, question 16
34Who is to condemn? Christ is the one who died, more than that, who was raised, who is at the right hand of God, who indeed intercedes for us.
14Therefore, having a great high priest who has passed through the heavens, Jesus the son of God, let us hold fast the confession. 15For we do not have a high priest unable to sympathize with our weaknesses, but one who has been tempted in every respect according to likeness, yet without sin. 16Let us therefore come near with boldness to the throne of grace, so that we may receive mercy and find grace for opportune help.
11If, on the other hand, perfection had therefore come through the Levitical priesthood, for the people had been placed under law upon it, there would still be need for another priest to arise according to the order of Melchizedek and not to be described according to the order of Aaron. 12For when the priesthood is changed, a change of law necessarily follows. 13For the one about whom these things are said belonged to another tribe, from which no one has served at the altar. 14It is obvious that our Lord has arisen from Judah, and in regard to that tribe Moses said nothing about priests. 15And it is still more evident if another priest arises according to the likeness of Melchizedek. 16He has become priest not according to a fleshly commandment of law but according to the power of an indestructible life. 17For it is testified: You are a priest forever according to the order of Melchizedek. 18On the one hand, a setting aside of the preceding commandment occurs because of its weakness and uselessness. 19For the law perfected nothing, but the introduction of a better hope does, through which we draw near to God. 20And inasmuch as this was not without an oath, for they have become priests without an oath 21But he became priest with an oath through the one who said to him, "The Lord has sworn and will not change his mind, 'You are a priest forever.'" 22Accordingly Jesus has become the guarantor of a better covenant to that extent. 23The former priests, on the other hand, were many because death prevented them from continuing. 24But because he remains forever, he holds the priesthood permanently. 25Consequently he is able to save completely those who draw near to God through him, since he always lives to intercede for them. 26For it was fitting that we should have such a high priest, holy, innocent, undefiled, separated from sinners, and exalted above the heavens. 27He does not have daily necessity, as the high priests do, to offer sacrifices first for his own sins and then for the sins of the people, because he did this once for all when he offered himself. 28For the law appoints men as high priests who have weakness, but the word of the oath, which came after the law, appoints a Son who has been perfected forever.
1My little children, I am writing these things to you so that you may not sin. And if anyone sins, we have an advocate with the Father, Jesus Christ the righteous. 2And he himself is the propitiation for our sins, and not for ours only but also for the sins of the whole world.
This question fills out what it means for Christ to be "seated at the right hand of the Father." The answer is drawn almost word for word from Hebrews 7:24-25, and the church's own standard says the same thing in a single clause: Article II of the Confession of Faith calls Jesus "eternal Savior and Mediator, who intercedes for us." The title "great high priest" comes from Hebrews 4:14, and the catechism uses it to teach that the ascended Christ is still at work on behalf of his people.
Because Jesus lives forever, he has a permanent priesthood is the argument of Hebrews 7. The priests of Israel "were many because death prevented them from continuing" (Hebrews 7:23), and they had "to offer sacrifices first for his own sins and then for the sins of the people" (Hebrews 7:27). Jesus is a priest of a different order, "according to the power of an indestructible life" (Hebrews 7:16), appointed by God's oath: "You are a priest forever according to the order of Melchizedek" (Hebrews 7:17). "Because he remains forever, he holds the priesthood permanently" (Hebrews 7:24). His sacrifice was made "once for all when he offered himself" (Hebrews 7:27), which is why Article XX of the Articles of Religion teaches that the offering of Christ, once made, needs no repetition.
He is able to save completely those who come to God through him, because he always lives to intercede for them is Hebrews 7:25 itself. Paul asks who could condemn the believer when Christ, who died and was raised, "is at the right hand of God, who indeed intercedes for us" (Romans 8:34). John gives the same comfort to Christians who have sinned: "we have an advocate with the Father, Jesus Christ the righteous. And he himself is the propitiation for our sins" (1 John 2:1-2). The priest who pleads for sinners is the one who "has been tempted in every respect according to likeness, yet without sin" (Hebrews 4:15).
For a Methodist this is the doctrine behind bold prayer. Hebrews draws the conclusion directly: "Let us therefore come near with boldness to the throne of grace, so that we may receive mercy and find grace for opportune help" (Hebrews 4:16). Wesley taught that the believer approaches God through the merits of Christ alone, and the church's prayers of confession and the Lord's Supper both rest on this one priest whose intercession never lapses (Hebrews 7:25).