What is the law during the time of Melchizedek?

OP: Accordingly, the change in law refers to a change from the law given during the priesthood of Aaron and back into the law given during the priesthood of Melchizedek."

Not necessarily. The verse Heb 7:12 For the priesthood being changed, there is made of necessity a change also of the law. says the priesthood has changed from Aaronic to Melchizedekian, but there is nothing to suggest the law referred to means the same as some unknown written law in the time of Melchizedek.

Nevertheless, if we keep reading, we find these answers about how the law has changed.

• Old Law: Aaronic descent (bloodline) only

• New Law: Whosoever

• Old Law: from a carnal (fleshly, bloodline) command

• New Law: endless life

• Old Law: weak and unprofitable

  New Law: better hope based on God's oath

  Old Law: no guarantee

• New Law: Jesus High Priest is the surety

  Old Law: changing priests

• New Law: eternal High Priest Jesus

• Old Law: daily presentations for sin

• New Law: one sacrifice once for sin

What is the law during the time of Melchizedek?

The following interpretation is based on the 2012 NICNT commentary on the Epistle to the Hebrews by Gareth Lee Cockerill.

The pastor in the book of Hebrews understood Melchizedek of Genesis 14:17-24 as the "Priest of the Most High God" (Heb 7:3) who is greater than the Levitical priestly order (Heb 7:1-10). This pastor also interpreted Ps 110:4 as God's declaration of the Son's (Jesus Christ's) priesthood (Heb 5:5-6, 10; 6:20).

Therefore, it's quite straightforward that the law changed from the Mosaic Law to the New Covenant Law. We shouldn't see the law as going "back" because as the order of Melchizedek interpreted this way is eternal, the New Covenant law is eternal as well. Although the pastor's assertion would shock Jews such as Philo or the Pharisees (who see Mosaic law as eternal), the Hebrews pastor is teaching the other way around: that the Mosaic law has been fulfilled in Christ, and in fact the Mosaic law is foreshadowing Christ's New Covenant law, which is the one that is eternal.

From Gareth L. Cockerill's commentary on Heb 7:12:

... Life under the law was dependent on the functioning of the Aaronic priesthood. Therefore, “a change of the priesthood” is necessarily a “change of the law.”²⁰ Thus the pastor would substantiate from the OT alone, without reference to Christ, that the prophesied change of priesthood anticipated a radical alteration in the relationship between the law and the people of God. This contention would shock those like Philo or the Pharisees who held that the law was eternally immutable²¹. And yet, as will become evident in the following verses, the pastor is convinced that fulfillment in Christ reveals what the law was always intended to be—not a means of approaching God but a God-instituted type and foreshadowing of the sufficient means of atonement and approach that would be provided by Christ.²²

This interpretation is consistent with Aquinas's Summa theologiae, I-II, q. 107, a. 1: Is the New Law different from the Old Law. Aquinas reconciles Mosaic Law and New Covenant Law by explaining that they are the same in one respect (that the purpose is to help us to submit the same God) but different in another respect (Mosaic law was intended as teacher of children, while the New Covenant law as teacher of grown adults).

It seems that the New Law is not different from the Old Law:

...

But contrary to this: In Hebrews 7:12 the Apostle says, “When the priesthood is transformed, it is necessary for a transformation of the Law to be made.” But as the Apostle proves in the same place, the priesthood of the New Law is different from the priesthood of the Old Law. Therefore, the Laws are likewise different.

I respond: As was explained above (q. 91, a. 4), all law directs human interaction in relation to some end. Now there are two ways in which things that are ordered to an end can be differentiated with respect to the notion of an end. First, they can be differentiated by the fact that they are ordered to diverse ends, and this is a difference in species, especially if the end is a proximate one. Second, they can be differentiated by their closeness to or distance from the end itself. For instance, it is clear that two movements differ in species insofar as they are ordered to different termini; on the other hand, to the extent that one part of a given movement is closer to the terminus than another part, there is a difference within the movement with respect to the perfect and the imperfect.

So, then, two laws can be differentiated in two ways.

In one way, they are differentiated in the sense of being wholly diverse, insofar as they are ordered toward diverse ends. In the case of cities, for instance, a law that was ordered toward rule by the common people (populus) would be different in species from a law that was ordered toward rule by the aristocrats (optimates) in the city.

In the second way, two laws can be differentiated by the fact that the one of them orders things more closely to the end, while the other orders things more remotely. For instance, in one and the same city, a law imposed on grown men (viri perfecti), who are capable of immediately doing what contributes to the common good, is different from a law meant to teach children, who have to be instructed in how to perform the acts of men later in life.

Therefore, one should reply that, according to the first way of differentiating laws, the New Law is not different from the Old Law, since both have the same end, viz., that men should submit to God, and there is just one God for both the New Covenant and the Old Covenant—this according to Romans 3:30 (“There is one God who justifies circumcision on the basis of faith and the lack of circumcision through faith”).

According to the second way of differentiating laws, the New Law is different from the Old Law. For the Old Law is, as it were, a teacher of children, as the Apostle says in Galatians 3:24, whereas the New Law is a law of perfection, since it is a law of charity. On this score, the Apostle says in Colossians 3:14 that the New Law is a “bond of perfection.”

Would you agree that the law Abraham obeyed (Gen. 26:5) is already the “eternal” New Covenant Law? This is considering that Abraham and Melchizedek were contemporaries (Genesis 14).

Under this interpretation, everyone, not just Abraham, already had this law written in their conscience, which can also be called 'natural law' which God put as part of human nature created in the image of God. When Jesus came, this natural law was being made more explicit in his Sermon on the Mount as well as in other books of the NT, to which we name 'New Covenant Law'. The explication of 'natural law' in OT (Mosaic law) and NT (New Covenant Law) is necessary since human corruption clouds our conscience. Therefore, I think Gen 26:5 is referring to this 'natural law' (or we can say, 'creational ethic', see this article).

I don't think Gen 26:5 should be linked to Melchizedek. Abraham would see Melchizedek as a mysterious figure, identified as Christ only much later. It's possible that Melchizedek taught Abraham "my commandments, my statutes, and my laws.", but this is speculation. "Abraham obeyed my voice" most likely refers to Abraham's obeying the specific call for him (by faith) to leave Haran to go to Canaan, to accept the Abrahamic covenant, and to later sacrifice Isaac.

Did Abraham Keep the Same Commandments God Gave to Moses?, answers a similar question:

Most religious teachers say that God's commands given through Moses applied only to ancient Israel and are not for us today.

But in drawing that conclusion, most of them overlook the full significance of what God said about Abraham's obedience in Genesis 26:5, hundreds of years before God spoke to Moses and Israel at Mt. Sinai: "Abraham obeyed me and kept my requirements, my commands, my decrees and my laws" (NIV).

The Hebrew words God uses here are especially important. As The Expositor's Bible Commentary explains regarding this verse: "The Lord then added a remarkable note: Abraham 'kept my requirements [mismarti], my commands [miswotay], my decrees [huqqotay] and my laws [wetorotay]' (v. 5).

"It is remarkable that this is precisely the way in which obedience to the Sinai Covenant is expressed in Deuteronomy 11:1: 'Love the Lord your God and keep his requirements [mismarto], his decrees [huqqotayw], his laws [mispatayw] and his commands [miswotayw]' . . .

"Thus Abraham is an example of one who shows the law written on his heart (Jeremiah 31:33). He is the writer's ultimate example of true obedience to the law, the one about whom the Lord could say, 'Abraham obeyed me' (v. 5). Thus, by showing Abraham to be an example of 'keeping the law,' the writer has shown the nature of the relationship between the law and faith. Abraham, a man who lived in faith, could be described as one who kept the law" (Vol. 2, 1990, pp. 186-187, emphasis added).

Abraham obeyed the same foundational spiritual laws that were given later to Israel. However, the symbolic tabernacle or temple ceremonies and rituals and Israel's national administrative laws were not applicable in Abraham's day. Nor are they necessary for individual Christians today, because a physical temple is no longer the center of our worship as it was in the ancient nation of Israel (John 4:19-21; Hebrews 9:9-10).

Thus, Abraham knew a lot more about God's requirements for and definitions of righteous behavior than most religious teachers give him credit for today. It also means that the laws defining righteous attitudes and behavior that were given to Israel were known and practiced by servants of God long before the Sinai Covenant was ever established.

Again, this shows that God's spiritual laws have always been in effect, even if not known by the people at various times.

Laws about the Levitical priesthood were exactly that, for the priesthood so that it could perform animal sacrifices symbolic of Christ's eventual sacrifice, ceremonies that were no longer needed once the final sacrifice had been made.

Similarly the civil laws were for the running of the Israelite government and society so that they could set an example (both good and bad) for the rest of the world to see.

But God's spiritual laws have always been in effect. They do not change.

Is there any reason to believe that "when the priesthood is changed, the law must be changed" refers to anything other than this one aspect of the law?:

[A high priest] who does not need daily, as those high priests, to offer up sacrifices, first for His own sins and then for the people’s, for this He did once for all when He offered up Himself. For the law appoints as high priests men who have weakness, but the word of the oath, which came after the law, appoints the Son who has been perfected forever.
— Hebrews 7:27–28

Notice what the change is: "… the law appoints … men … but the word … appoints the Son … ."

That is, there is no longer any need for the levitical priesthood, and in particular there is no longer any need for the daily sacrifices.

The levitical sacrifices of animals were prophetic symbols of the ultimate sacrifice of Christ. Now that this has happened, the symbolism has been superseded by the reality.

That is the how "the law must be changed".