It is "Paul, The Apostle to the Gentiles" (Rom 11:13) who plainly tells us that we who are of the Gentile "body of Christ" are NOT God's covenant people at all. Here below you see that the Gentiles were without any "covenant of promise."

"Wherefore remember, that ye being in time past Gentiles in (or according to) the flesh (race), who are called Uncircumcision ...12 ... at that time ye were Without Christ, being Aliens from The Commonwealth of Israel, and STRANGERS FROM THE COVENANTS OF PROMISE (given to Israel), having NO HOPE, and WITHOUT GOD in the world:" (Ephesians 2:11-12)

The "New Covenant" actually and fully applies ONLY to Israel as the ONLY Covenanted people of the Lord. However, though the "New Covenant" doesn't apply to the members of then Gentile "the body of Christ" in all its detail, as it will to a believing Israelite in the Kingdom, there are some aspects of the "New Covenant" that do apply to the members of "the body of Christ." Those aspects of the "New Covenant" that do apply to "the body of Christ" are what I call some of the "Blessings" of the "New Covenant" that spring from the cross, which Israel will fully enjoy in the coming Kingdom on earth during the Millennium.

The Blessings of the "New Covenant" that members of "the body of Christ" enjoy today are these.

Believers today live under grace and enjoy;

•  the freely given love and grace of God seen in our redemption, reconciliation, salvation is found only by faith in Christ - without works (Titus 3:5).
• We are now freed from the Penalty for Sin (Rom 3:24-26) and the Power of the Sin-nature (Eph 2:3) that indwells the flesh (Rom 6:14, 8:3) of all men until their physical death, or when they are Raptured to dwell eternal in the heavens (2Cor 5:1b).
• We enjoy the indwelling literal deposit of Christ (Col 1:27) in the form of "the Spirit of life in Christ Jesus" (Rom 8:2, cf., 1Cor 15:45) to be our new and abiding Life and life supply (Gal 2:20).

By His indwelling Spirit we of the "body of Christ" are fully equipped with Christ's "life" (Col 3:4a) and "we have the mind of Christ" (1Cor 2:16). By these blessings we are enabled to cope, endure, and work out the details of this life on earth in righteousness, even in the face of adversity... with peace and rest. The trials of life prepares us for living and "reigning" (2Tim 2:12) with Christ "eternal in the heavens" (2Cor 5:1).

Note that Paul says he was an Israelite "born out of due time (Gk. ektroma, untimely born)" (1Cor 15:8). Paul is saying he, an Israelite by race, was blessed to receive regeneration and be indwelled by the resurrection life of Christ during this Gentile age of grace. The "body of Christ" also enjoys these Blessings of the "New Covenant" outside of "due time," as it were, that is we enjoy these blessings earlier than when Israel, who will later enjoy these blessings in the Millennial Kingdom on earth. The Gentiles enjoying the blessings of the "New Covenant" before Israel is much the same as Paul was also blessed before Israel even though he was an Israelite. Paul as a Christian didn't have to wait to receive the Messiah and the Blessings of the "New Covenant" with the Israel later, in "the Kingdom." Israel will ultimately enjoy the fullness of the "New Covenant," but only at the time of the "1st Resurrection" to the kingdom (Rev 20:6), which will occur with 2nd coming of Christ and the establishment of His Millennial Messianic Kingdom reign on earth.

How is this "new covenant" to be a "Better Covenant" (Heb 8:6) for the believers of Israel?

As we've already stated, Jesus of Nazareth came addressing only "the lost sheep of the house of Israel" (Matt 15:34) in His earthly or terrestrial ministry to "the circumcision" (Rom 15:8). This was while Israel was still under the "Old Covenant" of the Mosaic "Law," which Jesus fully supported (cf., Luke 24:44). Yet, Jesus spoke concerning a time coming when the "kingdom of heaven" would come on earth, when believing Israelites... Would Innately Know the Lord and The Things of God By The Deposit of His "Spirit of Truth." Then they would Know Him Inwardly, Innately and Without having Received Teaching.

The Greek word for this kind of "unlearned knowledge" is "eido," meaning to "know' innately, by any of the senses," in this case we "know" by the inner sense of the "Spirit." Just as we have awareness by innate physical senses, so it is that believers have "knoweldge" by "the Spirit of truth" indwelling them.

The Hebrews writer wrote that believing Israelites will have innate knowledge of the Lord indwelling them in the coming Kingdom and none will need it taught to them.

"And They (Israel in the kingdom) Shall NOT TEACH Every Man His Neighbour, and every man his brother, saying, Know the Lord: for ALL SHALL KNOW (Gk., eido) ME, From The Least To The Greatest. (Heb 8:11)

Jesus also promised this kind of "knowledge (eido)" that does not require teaching (Heb 8:11 below).

"Even the Spirit of truth; whom the world cannot receive, because it seeth him not, neither knoweth him: but ye know (Gk. eido) him; for He Dwelleth With You, and (the Spirit of Truth) Shall Be IN YOU. (John 14:17)

These verses above are confirmed by Ezekiel's prophecy concerning believing Israel's intimate relationship with the Lord that is yet to come to Israel in the promised Kingdom.

26 A New Heart Also Will I Give You (believing Israel), and a New Spirit Will I Put WITHIN YOU: ... 27 And I Will Put My Spirit WITHIN YOU, And Cause You To Walk In My Statutes, And Ye Shall Keep My Judgments, And Do Them. 28 And ye shall dwell in the land (of Israel) that I gave to your fathers; and ye shall be my people, and I will be your God. (Ezekiel 36:25-28)

In "the kingdom" the believers of the Nation Israel will possess Christ's "Spirit of truth" by His very "Spirit of life" within them... teaching them inwardly.

John wrote this below in his first epistle to the scattered of Israel, to whom Jesus said he was to direct his ministry (Matt 10:5-6). John wrote concerning this blessing of innate knowledge of God that Messianic believing Jews of his time possessed by the inbreathed spirit (John 20:20), and that all believing Israelites will enjoy in the coming Kingdom. This refers to a time after they've believed to receive Christ's life into them by faith, now to be during the Tribulation and the Millennial Kingdom.

20 But ye have an unction (anointing) from the Holy One (Christ), and Ye Know all Things. (1John 2:20)
27 But the (Spirit) anointing which ye have received of him (Christ) abideth IN YOU, and ye need not that any man teach you: but as the same anointing teacheth you of all things, and is truth, and is no lie, and even as it hath taught you, ye shall abide in him. (1 John 2:27)

Thankfully, we today as the genuine rebirthed members of "the church, which is His body" already possess the "Spirit of Christ" within us, teaching and guiding us inwardly, as He will Israel in "the Kingdom."

"...I (Paul) am made a minister, according to the dispensation of God which is given to me (Paul) for you, to fulfil (complete)the word of God; 26 ...the Mystery which Hath Been Hid from ages and from generations, but Now Is Made Manifest to his saints (believers): 27 To whom God would make known what is The Riches Of The Glory Of This Mystery Among The Gentiles; Which Is CHRIST IN YOU, the hope of glory:" (Col 1:25-27).

With Israel's full rejection of Christ and the resultant temporary "blindness" upon Israel during this age of "grace" (Rom 11:25, cf., 2Cor 3:14), the "blessings of" the "New Covenant" are now bestowed freely upon the Gentiles "to provoke them (Israel) to jealousy" (Rom 11:11).

So it is that we of "the body of Christ"  today are NOT covenant people as Israel is, we do enjoy the blessings of the "New Covenant" with regard to Christ's indwelling "life" (Col 3:4a) and nature, and we thereby have the innate indwelling knowledge of the resurrected Lord.

Thus Paul wrote that "we have the mind (Gk. gnosis, intellect) of Christ" Himself working within us (Philippians 2:13). All we needed was to receive salvation in Christ... with His life; and then to trust this new inner sixth sense we have by Christ's indwelling Spirit speaking within our human spirits to guide and empower us in our living (cf., Rom 8:9-10, 1Cor 6:17, Gal 2:20).

".... we have the mind (Gk. gnosis, intellect) of Christ (in our spirit)" (1Corinthians 2:16b).

"For it is God which worketh IN YOU both to will and to do of his good pleasure." Philippians 2:13.