⁶(God) Who also hath made us (the body of Christ) able ministers of the New Testament (Covenant); not of the letter (Law), but of the spirit: for the letter killeth, but the spirit giveth life. 2 Corinthians 3:6

Does the New Covenant apply to the Israel only or to the "body of Christ," or to both?

Israel, not the Gentiles, was the recipient of the Old Covenant. Some then consider that, logically, the New Covenant belongs to Israel and not the Gentiles. But how do we reconcile that thought with Paul's clear words seen above in 2Cor 3:6, written to the members of the predominantly Gentile "body of Christ." The "body of Christ" consists of "all men," that is both Jew and Gentile, but wherein Paul says "there is neither Jew nor Gentile" because "all are one in Christ" (Gal 3:28)? The "body of Christ"  observes no distinction between Jew and Gentile - all are as Gentiles. Paul in fact is "THE Apostle to the Gentiles" (Rom 11:13). Paul says we know no man "after the flesh" (2Cor 5:16a).

Many believers, including many right dividing grace believers, are confused over the place of Paul's doctrine of the New Covenant.

The "body of Christ" does in fact fall under the umbrella of the New Covenant, but in a different way than Israel does.

Paul clearly teaches in Romans that we are partakers of Israel’s spiritual blessings (Rom. 15:27 cf. Eph. 1:3-14).

²⁷ It hath pleased them verily; and their debtors they are. For if (Gk., ei, and that) the Gentiles have been made partakers of their (Israel's) spiritual things, their duty is also to minister unto them in carnal things. Romans 15:27

There is absolutely no possibility that this could refer to anything other than the New Covenant. One thing that should never be overlooked, however, is the fact that Israel received it by promise whereas we, the body of Christ, are the glad recipients of it by grace (Jer. 31:31 cf. Titus 2:11).

³¹ Behold, the days come, saith the Lord, that I will make a new covenant with the house of Israel, and with the house of Judah: Jeremiah 31:31

¹¹ For the grace of God that bringeth salvation hath appeared to all men, Titus 2:11

As we know, one of the principal blessings of the New Covenant is the precious "blood of Christ." This particular key element can never be divorced from the covenant nor should it be. If the "Body of Christ" has no connection to this covenant whatsoever, then our Savior must return a second time to die for the Gentiles. This cannot be since Christ died “once for all” (Heb. 10:9-12).

Who could fail to see that Paul charges us to remember the blood of this New covenant until the Lord comes.

“This cup is the New Testament (Covenant) in my blood: this do ye… in remembrance of me. For as often as ye (the members of His Body) eat this bread and drink this cup, ye do show the Lord’s death till He come” (I Cor. 11:23-26).

Furthermore, the New Covenant shows that there is a connection between the two distinct programs of God (Israel's and that of the "body of Christ"), which highlights His eternal purpose to recover and reconcile "all things in Christ."

¹⁰ That in the dispensation of the fulness of times he might gather together in one all things in Christ, both which are in heaven, and which are on earth; even in him: Ephesians 1:10

He Truly is Lord of all.