Yes He is seated, in heaven, but as you can see below, He is also performing His priestly service to the Father. He is a priest in the order of Melchizedek, who offered bread and wine. Jesus at the last supper, offered himself as the unblemished Lamb of God. His offering to the Father started in the upper room, where He initiated the New Covenant in His Blood. That same offering continued through His passion and death and still continues in heaven, without end.
Hebrews 8
New King James Version (NKJV)
The New Priestly Service
8 Now this is the main point of the things we are saying: We have such a High Priest, who is seated at the right hand of the throne of the Majesty in the heavens, 2 a Minister of the sanctuary and of the true tabernacle which the Lord erected, and not man.
3 For every high priest is appointed to offer both gifts and sacrifices. Therefore it is necessary that this One also have something to offer. 4 For if He were on earth, He would not be a priest, since there are priests who offer the gifts according to the law; 5 who serve the copy and shadow of the heavenly things, as Moses was divinely instructed when he was about to make the tabernacle. For He said, “See that you make all things according to the pattern shown you on the mountain.”[a] 6 But now He has obtained a more excellent ministry, inasmuch as He is also Mediator of a better covenant, which was established on better promises.
But when Christ came as high priest of the good things that are now already here, he went through the greater and more perfect tabernacle that is not made with human hands, that is to say, is not a part of this creation. 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. The blood of goats and bulls and the ashes of a heifer sprinkled on those who are ceremonially unclean sanctify them so that they are outwardly clean. How much more, then, will the blood of Christ, who through the eternal Spirit offered himself unblemished to God, cleanse our consciences from acts that lead to death, so that we may serve the living God! For this reason Christ is the mediator of a new covenant, that those who are called may receive the promised eternal inheritance—now that he has died as a ransom to set them free from the sins committed under the first covenant.
In the case of a will, it is necessary to prove the death of the one who made it, because a will is in force only when somebody has died; it never takes effect while the one who made it is living. This is why even the first covenant was not put into effect without blood. When Moses had proclaimed every command of the law to all the people, he took the blood of calves, together with water, scarlet wool and branches of hyssop, and sprinkled the scroll and all the people. He said, “This is the blood of the covenant, which God has commanded you to keep.” In the same way, he sprinkled with the blood both the tabernacle and everything used in its ceremonies. In fact, the law requires that nearly everything be cleansed with blood, and without the shedding of blood there is no forgiveness.
It was necessary, then, for the copies of the heavenly things to be purified with these sacrifices, but the heavenly things themselves with better sacrifices than these. 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. Nor did he enter heaven to offer himself again and again, the way the high priest enters the Most Holy Place every year with blood that is not his own. Otherwise Christ would have had to suffer many times since the creation of the world. But he has appeared once for all at the culmination of the ages to do away with sin by the sacrifice of himself. Just as people are destined to die once, and after that to face judgment, so Christ was sacrificed once to take away the sins of many; and he will appear a second time, not to bear sin, but to bring salvation to those who are waiting for him. (Hebrews 9:11-28)