How do the Levitical priests relate to Jesus’ priesthood “after the order of Melchizedek”?

It is really key in the book of Hebrews that Christ has a priesthood that is superior to the Levitical priesthood. He could not have been of the tribe of Levi, and it is important that His priesthood is of the order of Melchizedek.

I think Jeremiah was using the categories of the law when writing about the Levitical priesthood (Jer. 33:18). The law was set up on Mount Sinai. The LORD said in Exodus 25:9 and 25:40, “You shall make the tabernacle and all its furnishings according to the pattern shown you on the mountain.” Therefore, what was happening in the tabernacle and what the Israelites did in the law—how they planted their fields, what type of clothes they wore, and so on—were an earthly copy of a heavenly reality. We see several times in Scripture that the Levitical priesthood was created to be a copy on earth of a heavenly reality. In and of itself, it was not the real, ultimate, heavenly priesthood. This idea is picked up in Hebrews 8:1–5, where we read that we have such a great High Priest who is in heaven, not like the Levitical priests who served as a copy and shadow of what is in heaven.

To talk about a continual priesthood in the terms of the law means talking about a continual Levitical priesthood, which is the copy of the heavenly reality. That is the terminology that the law uses. The Levitical priesthood, however, is a copy and shadow of the reality of heavenly priesthood, which is found exclusively in Christ. There are not two eternal priesthoods but one—Christ’s heavenly priesthood after the order of Melchizedek.