In Jeremiah 31:31 we see Yah renewing, restoring, or refreshing - not replacing - the covenant with his people. So why do we express the covenant in such terms?
While there are a myriad of answers that may be given to support the above statement, time and space limit me to but a few: Term, Time, and Text. I will also make a few statements concerning the Covenant of Grace.
The Term - "New"
Both the Hebrew chadash (Jer. 31:31) and the Greek kainos (Heb. 8:8) words for "new" may be more properly translated "renewed" as opposed to "new" or "brand-new" in certain contexts.
Chadash may mean new in quality, not new in time (1 Sam. 11:14; 2 Chron. 15:8; 24:4, 12; Job 10:7; Psa. 103:5; 104:30; Isa. 61:4; Lam. 5:21). It may also mean to "renew" or "repair". For instance, in Psalm 51:10 David says, "Create in me a clean heart, O God; and renew a right spirit within me." David uses the same word as in Jeremiah 31:31 (chadash). David was not asking for something brand-new, but was asking for a renewal of what he had previously. In 2 Chronicles 24:4, 12 we see the use of the terms repair and restore (root, chadash) with the already existent house of Yah. So, in all these verses, there is a renewal, a repairing, a restoring of that which was already in existence. The same is true for Jeremiah 31.
In the New Testament, of the eight times that "new" is applied to the New Covenant, seven of them use the term kainos - meaning "renewed," or "new in quality," not necessarily time (Matt. 26:28; Mark 14:24; Luke 22:20; 1 Cor. 11:25; 2 Cor. 3:6; Heb. 8:13; 9:15) as opposed to neos (meaning new in time - Heb. 12:24). The use of term kainos means there was a pre-existing covenant to which Yahusha gave a qualitative difference.
We see the use of kainos more clearly in such verses as John 13:34, where the commandment to love one another was not brand-new (i.e. neos). After all, this commandment was the very heart of the Old Covenant (Lev. 19:18; et al.); Yahusha simply added a new quality to the Old Covenant command, "as I have loved you". Another example may be helpful: When Paul was preaching Yahusha, some accused him of preaching a new doctrine (Acts 17:18-19). Here, the doctrine of Messiah was not brand-new and had been around for some time - and not only in the New Testament (Gal. 3:8). However, it was unfamiliar to his present audience, therefore this was kainos, not neos.
As to the one verse that uses neos to describe the New Covenant (Heb. 12:24), it simply means Yahusha was the "brand-new" (neos) Administrator of the re-newed (kainos) covenant (as opposed to Moses some two thousand years earlier). This is brand-new and makes the covenant re-newal possible.
Some attempt to make the case that since the New Covenant has a better sacrifice (Heb. 9:23), mediator (Heb. 8:6; 9:15, 24; 12:24), ministration in the spirit (2 Cor. 3:6), high priest (Heb. 7:24-28; 8:1-6), priesthood after the order of Melkizedek (Heb. 7), promise (Heb. 7:24-25; 8:5; 9:1), and tabernacle made without hands (Heb. 8:1-6; 9:11, 24), this New Covenant must mean brand-new. However, the covenant with Moses is not obsolete (Heb. 8:13) in the sense it has no value. After all, Yahusha, the administrator of the New Covenant, embraced the Old as relevant and even taught it to his disciples. Similarly, the Ten Commandments still have relevance today (Matt 22:36-40). However, the Old Covenant is obsolete from the standpoint that Messiah's priesthood has superseded its priestly institutions.
Jeremiah and the author of Hebrews both spoke about a covenant already in existence, but that became re-newed in character or quality and not one that was absolutely brand-new. The eternal covenant (Gen. 17:9-13) became renewed in Messiah (Rom. 15:8-9).