“We do have such a high priest, who sat down” In comparison to the old order where the furnishings of the Tabernacle did not include any seats or chairs and the priest’s work was never finished, serving in the Tabernacle from sunrise to sunset; our High Priest – Jesus Christ – finished the work He came to do and sat down in the glory (the Most Holy Place). 
“.. who serves in the sanctuary, the true tabernacle.” Christ serves in the true Sanctuary / Tabernacle that has been set up by The Lord Himself, and again in comparison to the old order, the high priest briefly entered the Holy Place of the Tabernacle once a year with the blood of the atonement ; but after He offered the eternal sacrifice, our Great High Priest dwells forever in the heavenly sanctuary as our intercessor .
“.. so it was necessary for this one also to have something to offer.”  One of the duties of the high priest was to offer to God the gift brought by an Israelite to the Tabernacle/Temple in atonement for their sin, and so it was necessary for Christ to offer atonement to God on our behalf. 
“If he were on earth, he would not be a priest…”  The fact that Our Lord did not descend from the tribe of Levi disqualified Him from becoming a high priest in the earthly temple. But “..the ministry Jesus has received is as superior to theirs…” Jesus is a superior priest and has a superior ministry; “as the covenant of which he is mediator is superior” and has a superior priesthood – a superior covenant.  The old and ineffective covenant has been replaced by a new efficient covenant, seeing that the in the old covenant the Law itself is holy and good but was unable to provide the power over sin for the sinner and was unable to free the sinner of sin, therefore, something better than the law was necessary. 
A new covenant is introduced  whereby God’s laws will become inner principles of the heart, empowering and enabling the sinner to delight in doing God’s will, the sinful ignorance of God will be removed and all believers will know God personally, and God will forgive our iniquities (full atonement) and will choose not to remember our sins. This was not possible under the old covenant. The new covenant has made the old covenant obsolete  which indicates that the old covenant was not permanent, and that it was intended to disappear; to revert back to the old covenant would be to go back to something that is no longer valid.
Therefore, we need to recognize that Our Heavenly High Priest – Our Lord Jesus Christ – is superior to the old order of priesthood; and that the new covenant, which he instituted, replaces the old covenant that could not clear the guilty conscience of the sinner.