The old priesthood required that priests should only belong to the tribe of Levi but Christ came not belonging to Levi but was from the tribe of Judah. For not to confuse us God removed the levitical priesthood and all it's requirements. I said all it's requirements, to include "also ordinances of divine service, and a worldly sanctuary" (Heb 9:1). All were done away with.
There is no way you can understand the new priesthood from the old; whether it's about sacrifices and/or serving God. "Which was a figure for the time then present, in which were offered both gifts and sacrifices, that could not make him that did the service perfect, as pertaining to the conscience; Which stood only in meats and drinks, and divers washings, and carnal ordinances, imposed on them until the time of reformation." Hebrews 9:9-10
Hebrews 7:12 says, "For the priesthood being changed, there is made of necessity a change also of the law."
We've to understand that Jesus did not become a priest by meeting the old requirements of the law - he is a testator! It was by appointment.
When God sent JESUS as a new kind of priest He needed him to be priest for ever! No more he was going "...to take tithes of the people according to the law..." (Hebrews 7:5). Be careful how and whom you pay your tithes too. If you do it to help the brethren then you're lost. Pay it to Melchizedek, i.e., a person who lives forever, is exalted into the heavens and has the power to bless you. "For Christ is not entered into the holy places made with hands, which are the figures of the true; but into heaven itself, now to appear in the presence of God for us..." Hebrews 9:24
In order to appear before God, Hebrews 8:3 says, "every high priest is ordained to offer gifts and sacrifices: wherefore it is of necessity that this man have somewhat also to offer."
"...But into heaven itself, now to appear in the presence of God for us..." (Hebrews 9:24), with his own blood, not of animals, not gold or silver, but his own blood. He established for us a new kind of worship.
I love this;
"Having therefore, brethren, boldness to enter into the holiest by the blood of Jesus, By a new and living way, which he hath consecrated for us, through the veil, that is to say, his flesh; And having an high priest over the house of God; Let us draw near with a true heart in full assurance of faith, having our hearts sprinkled from an evil conscience, and our bodies washed with pure water. Let us hold fast the profession of our faith without wavering; (for he is faithful that promised;)" Hebrews 10:19-23