That is a very different question. The author of Hebrews stated the big picture – making offering for sins. Christians take this as a foreshadowing of the fulfillment by Christ, the eternal High Priest.
The levitical priesthood offered bloody animal sacrifices. Christ, “once for all” offers Himself and His blood at Calvary.
Thenceforth, Christ, Who is eternal, offers Himself eternally - without suffering and without blood - to the Father in love. The offering in time was at Calvary. The priestly people enter the eternal offering at Mass. The veil of time and space are rent; the ministerial priesthood presides with human hands in time and space but Christ Himself offers the Sacrifice of the Mass.
So to answer your question: the Priesthood of the Church is the fulfillment, in Christ, our Great High Priest, of what was shadowed by the levitical priesthood.
Even the layout of Catholic churches reflects this. Traditionally, the Tabernacle, where the consecrated Sacrament is kept, is in the position occupied by the Ark of the Covenant in the Temple. What’s in the Ark? The tablets of the Commandments, Aaron’s rod that budded, confirming his priesthood, and the last of the manna. What’s in the tabernacle: Jesus Christ: The living Word, the great High Priest, and the Bread of Life.