If the new covenant is not made with Christians, why is it referred to in one particular Christian book (Hebrews) more than anywhere else in the NT?

All covenants between God and man are for earth and not heaven. The word covenant is first mentioned in connection with Noah in Gen. 6: 18. What is said of that covenant in Gen. 9: 8–17 shows that it concerned the earth. God said “I set my bow in the clouds, and it shall be for a sign of the covenant between me and the earth” (v13, my emphasis). Seven times in this section we have the word covenant (vs 9, 11, 12, 13, 15, 16, 17) and seven times the word earth occurs (vs 10 (twice), 11, 13, 14, 16, 17), perfectly expressing the fact that covenants have the earth as their sphere. Subsequently, every covenant that God made with man involved the nation of Israel for all of Israel’s relationships with God and their blessings from Him have the earth as their sphere (see Deut. 28: 1–14). They have nothing to do with heaven and what is heavenly. The future new covenant is also to be made with Israel (see Jer. 31: 31–34). In sharp contrast to Israel, the Christian’s blessings are heavenly. We have been blessed “with every spiritual blessing in the heavenlies in Christ” (Eph. 1: 3) and “our commonwealth has its existence in [the] heavens” (Phil. 3: 20).

   The Hebrew Christians were Jews who had believed on Christ but were in danger of going back to Judaism—a religion whose relationships and blessings were earthly. Accordingly, the writer presents the thought of heaven and what is heavenly in Hebrews more than in any other epistle. The Jewish believers are addressed as “partakers of [the] heavenly calling” who “have tasted of the heavenly gift”, seek “a heavenly” (country) and have come to “heavenly Jerusalem” (Heb. 3: 1; 6: 4; 11: 16; 12: 22). Christ is presented to them as high priest who if “then indeed he were upon earth, he would not even be a priest” (Heb. 8: 4) but “who has passed through the heavens”, become “higher that the heavens”, “has sat down on [the] right hand of the throne of the greatness in the heavens” and has entered “into heaven itself” (Heb. 4: 14; 7: 26; 8: 1; 9: 24).

            The new covenant, prophesied in the OT (see Jer. 31: 31–34) is only introduced in Hebrews to prove that the conditional covenant of Sinai and the whole system connected with it was imperfect (see Heb. 7: 11, 18, 19). God had said of Israel “my covenant they broke” (Jer. 31: 32) and that “they did not continue in my covenant” (Heb. 8: 9). The very fact that there was to be a new covenant “made the first old; but that which grows old and aged [is] near disappearing” so God “takes away the first that he may establish the second” which is “eternal” (Heb. 8: 13; 10: 9; 13: 20).

   Any idea that the new covenant had been implemented when Hebrews was written is eliminated on its very first mention in the epistle where we read “by so much Jesus became surety of a better covenant” (Heb. 7: 22). The writer uses a word here that is found nowhere else in the NT. It is egguos, which means surety, pledge or security. When a pledge is given it means that what is pledged has not yet been received. This verse shows that Jesus is the guarantee of the future literal implementation of the new covenant with Israel. This singular fact is reinforced throughout by the writer’s careful use of pronouns such as us and them. Immediately before his quotation from Jeremiah, he says “For finding fault, he says to them” (Heb. 8: 8, my emphasis), making a distinction and a difference between Christian Jews (to which the epistle was written) and the nation. This distinction is even more apparent prior to his second quotation of Jer. 31 when he says the “Holy Spirit also bears us witness [of it]” (my emphasis) but in the quotation changes “the house of Israel”, not to ‘us’, but to “them”. (Heb. 10: 15, 16, my emphasis).

   It is the intrinsic value of the “blood of the Christ” alone that makes Him “mediator of a new covenant” (Heb. 9: 14, 15) generating the warning to the Hebrews professing faith of their esteeming “the blood of the covenant, whereby he has been sanctified, common” (Heb. 10: 29, my emphasis). It is the blood that sanctifies, not the covenant. Finally, in the list of things the Jewish Christians had “come to” (Heb. 12: 22–24) he does not say ‘we have come to a new covenant’ but “to Jesus, mediator of a new covenant; and to [the] blood of sprinkling, speaking better than Abel” (v24), that is to a Person and His blood. Features of the new covenant such as the remission of sins, knowledge of God, and the indwelling of the Holy Spirit, Christians have now as individuals, but Israel must wait for the return of Christ to enter into the fulness of the covenant nationally when they will dwell as God’s people in the land that He gave to their fathers (see Ezek. 36: 28).