Problem: The author of Hebrews writes, “He said, ‘A new covenant,’ He has made the first obsolete but whatever is becoming obsolete and growing old is ready to disappear” (Heb. 8:13). This Scriptural citation comes from Jeremiah 31:31-36, which is addressed to Israel and speaks of the messianic kingdom. Amillennial interpreters claim that this passage demonstrates that the church replaces the old covenant with a new covenant.
Solution: A number of observations can be made:
First, the author of Hebrews states that the MOSAIC covenant is obsolete—not the ABRAHAMIC covenant. Verse 9 states, “When I took them by the hand to lead them out of the land of Egypt.” This is not referring to Abraham; it is referring to Moses. While the law is obsolete for believers (c.f. Rom. 7:6), the promises to Israel through Abraham are still in effect.
Second, if this passage is for the church, then why are we still committed to evangelism? Not everyone on Earth has heard of the Lord today, and this is why the church is commissioned to evangelize. But the author of Hebrews quotes Jeremiah as saying, “They will not teach again, each man his neighbor and each man his brother, saying, ‘Know the Lord,’ for they will all know Me, from the least of them to the greatest of them” (Jer. 31:34). How could this passage refer to the church age, when many people on Earth have never heard of the Lord? This state of humanity will not occur until the millennium (c.f. Ezek. 34:25; Isa. 11:6-9).
Third, the author of Hebrews could be citing a partial fulfillment. The church receives the blessings of the Abrahamic covenant (Gal. 3:14; 4:22-31) without completely fulfilling that covenant. This would be an example of how a partial fulfillment does not invalidate a complete fulfillment. The church fulfills this promise in part, but Israel will fulfill this promise in whole. The author never says that the new covenant is in full force (or fully fulfilled), only that the old covenant has passed away. The author of Hebrews is not trying to discuss eschatology here; he is merely trying to convince his Jewish-Christian audience that the old covenant has passed away. In a similar way, I might make a contract to buy a house. My covenant is between me and the bank, but others could benefit from this covenant (e.g. guests who come over for dinner).
Fourth, the “new covenant” language could have two meanings. This could either refer to  a separate covenant for the church or  that the church was inaugurating a portion of the original covenant to Abraham. Jeremiah 31:31 states that the new covenant was specifically made with Israel (c.f. Ezek. 34:14; 36:22). Paul wrote that “all Israel will be saved” (Rom. 11:26). Jesus came specifically for the House of Israel (Mt. 10:1-6; 15:21-28). Let’s consider each possibility:
- Separate covenant: This is possible, because the church age was not revealed in the OT. It’s possible that when Jesus said, “This cup which is poured out for you is the new covenant in My blood” (Lk. 22:20 NASB), he was inaugurating a covenant, which had not been revealed thus far. In this case, Jesus’ new covenant had nothing to do with the “new covenant” of Jeremiah 31.
Portion of the original covenant: On the other hand, it is possible that the new covenant for the church is the inauguration of a portion of Jeremiah’s “new covenant.” Remember, a partial fulfillment does not invalidate a complete fulfillment.
 For more teaching on the “new covenant” see also Is. 24:5; 61:8; Jer. 32:40; 50:5; 1 Cor. 11:25; 2 Cor. 3:6; Heb. 8:8; 9:15; 13:20; Mt. 26:28; Mk. 14:24; Jn. 1:17; Rom. 11:27; Heb. 10:16; 12:24.
 Abraham’s descendent was promised to be a blessing to the Gentile nations. This was partially fulfilled in the time of Jonah. Jonah was a blessing to the Ninevites (a Gentile nation). And yet, no one would argue that Jonah’s partial fulfillment would invalidate a complete or ultimate fulfillment through Christ!
“In that he saith, A new covenant, he hath made the first old. Now that which decayeth and waxeth old is ready to vanish away. (Heb 8:13)”