The main point of what has been said is this: we have such a high priest, who has taken his seat at the right hand of the throne of the Majesty in heaven, a minister of the sanctuary and of the true tabernacle that the Lord, not man, set up. Now every high priest is appointed to offer gifts and sacrifices; thus the necessity for this one also to have something to offer. (Heb 8:1-3)
Jesus is a minister in the sanctuary offering up (present tense) His eternal sacrifice to the Father which is perfected in heaven.
Now he has obtained so much more excellent a ministry as he is mediator of a better covenant, enacted on better promises. (Heb 8:6)
The covenant Jesus mediates (present tense) is the covenant of His body and blood which He offers in the same manner as the bread and wine offered by Melchizedek.
Then he took the bread, said the blessing, broke it, and gave it to them, saying, “This is my body, which will be given for you; do this in memory of me.” And likewise the cup after they had eaten, saying, "This cup is the new covenant in my blood, which will be shed for you. (Luke 22:19-20)
This sacrifice is the Mal. 1:11 pure offering made present in every place from the rising of the sun to its setting in the Eucharist.
Therefore, it was necessary for the copies of the heavenly things to be purified by these rites, but the heavenly things themselves by better sacrifices than these. (Heb 9:23)
Through him (then) let us continually offer God a sacrifice of praise, that is, the fruit of lips that confess his name. (Heb 13:15)
The phrase “sacrifice of praise” refers to the “toda” animal sacrifices that had to be consumed. The Eucharist is the “toda” sacrifice of the New Covenant. The Eucharist also fulfills Jer. 33:18 that His kingdom will consist of a sacrificial priesthood forever, and fulfills Zech. 9:15 that the sons of Zion shall drink blood like wine and be saved.