Yes, He is our priest. However, Hebrews 8:4 is clear that His kingdom is not of this earth.
Heb 8.4 Now if He were on earth, He would not be a priest at all, since there are those who offer the gifts according to the Law; (NASB)
I don't see any textual evidence in this passage that supports your position that His kingdom is not of this earth. It does clearly imply that He is not physically on the earth right now. But the passage doesnt really address what you are claiming.
I would go back to the Davidic covenant and claim that that covenant is not fulfilled as of yet because the eternal earthly kingdom has not been initiated as of yet.
In fact, the Abrahamic covenant has not been totally fulfilled. If you look at the promised land boundaries that God promised to Abrahams descendents, not all that area mentioned has ever been possessed by the Jewish nation. Therefore, the full land boundaries that God promised Abrahams descendents will be realized sometime in the future.
Now some may say that the advent of the NT has nullified the need for the fulfillment of the Davidic covenant. But if you read Psalm 89, you cannot claim that God has replaced the Davidic covenant with something else.