Let’s define “covenant.”  The Hebrew word has its origin in a verb meaning ‘”to cut or divide’ in allusion to a sacrificial custom in connection with covenant making” (Vine’s).  The word is used of (1) Covenants between men – (a) a treaty, alliance, league; (b) constitution, ordinance between monarch and subjects; (c) agreement, pledge; (d) alliance of friendship; (e) alliance of marriage.  (2) Covenants between God and man – (a) alliance or friendship; (b) divine constitution or ordinance (B-D-B-G).

The Greek word means literally “through a receptacle, repository, chest, box.”  It is used of “a disposition of property by will or otherwise” (Vine’s).  It is also used of: (1) a disposition, arrangement; (2) a compact, covenant (Thayer).  The word is used by the Septuagint for the Hebrew word.  Another point to understand is that this word frequently refers to unilateral agreements or declarations.  “It is the declaration of one person’s will, not the result of an agreement between two parties” (B-A-G).

“Behold, the days are coming, says the Lord, when I will make a new covenant with the house of Israel and the house of Judah” (Jeremiah 31:31).

The writer of Hebrews quoted Jeremiah 31:31-34 (see Hebrews 8:7-13; 10:15-18).  He even said, “In that He says, ‘A new covenant,’ He has made the first obsolete” (Hebrews 8:13).

When did this covenant come?  Jesus connected this covenant with his blood (Matthew 26:28; Luke 22:20).  The Hebrews writer said, “where there is a testament, there must also of necessity be the death of the testator.  For a testament is in force after men are dead, since it has no power at all while the testator lives” (Hebrews 9:16-17).  The writer then connected these words with the sacrifice of Jesus (Hebrews 9:23-28).

Some have seen an allusion to a “last will and testament” in Hebrews 9:16-17; However, such is really not in view.  Consider these things: (1) the New Covenant is being compared to Moses’ giving of the Old Covenant.  There was no death of the testator in that covenant, if we mean by this the death of one who made out a “last will and testament.”  However, there was blood shed (cf. Exodus 24:1-8).  (2) The words “men” and “testator” do not appear in the Greek reading of Hebrews 9:16-17.  The words are supplied.  Adam Clark commented, “Where there is a covenant, it is necessary that the death of the appointed (victim) should be exhibited, because covenant is confirmed over dead (victims), since it is not valid while the appointed (victim) is alive” (Vol. 6, pg. 747-748).  The Zondervan Parallel New Testament in Greek and English reads, “For where a covenant death necessity to be offered of the making covenant, for a covenant over dead [is] firm, since never has it strength when lives the making covenant.”  (3) The comparison is this: Moses declared and then ratified, or instituted it with blood.  This is exactly what Jesus did.

“…not according to the covenant that I made with their fathers in the day that I took them by the hand to lead them out of the land of Egypt” (Jeremiah 31:32).

The words, “the day that I took them by the hand to lead them out of the land of Egypt” includes that which was engraved upon stones (see 1 Kings 8:9 cf. 8:21).  This covenant would be in some way(s) different from that covenant.

“But this is the covenant that I will make with the house of Israel after those days, says the LORD: I will put my law in their minds, and write it on their hearts; and I will be their God, and they shall be my people.  No more shall every man teach his neighbor and every man his brother saying, “Know the LORD, ‘for they all shall know me, from the least of them to the greatest of them says the LORD… I will forgive their iniquity, and their sin I will remember no more” (Jeremiah 31:33-34).

Here are the differences in the covenants…

1) The Israelites of old became Israelites  (God’s chosen people) by birth.  One became such without any knowledge of the LORD, or His law.  He had to be taught such things later by others.  Some Israelites did have God’s word in their hearts [(Psalm 37:41; 40:8; 119:11; cf. Deuteronomy 4:9-10; 6:6-7; 11:18-19; 30:14) and even some Gentiles (Romans 2:15)].  However, under this new covenant one must first know (cf. John 6:45).  Today, man is required to be “born again” (John 3:3-5).

2)  Sin under the previous covenant was remembered each year on the Day of Atonement (Hebrews 10:1-3 cf. Leviticus 16:11-15).  The sacrifice of Jesus is once and for all (Hebrews 9:25-26).  He remembers our sin no more (Hebrews 10:17-18).