The new covenant was obviously made for both the Jews and the Gentiles, but when the new covenant was announced something interesting happens.
For this is the covenant that I will make with the house of Israel after those days, saith the Lord; I will put my laws into their mind, and write them in their hearts: and I will be to them a God, and they shall be to me a people:
- Hebrews 8:10 (KJV)
It doesn't actually say "Jews and Gentiles", but instead it just says "house of Israel". So what about the Gentiles?
As of the new covenant Israel is no longer bound to just physical Israel.
Not as though the word of God hath taken none effect. For they are not all Israel, which are of Israel: Neither, because they are the seed of Abraham, are they all children: but, In Isaac shall thy seed be called.
- Romans 9:6-7 (KJV)
We become "Jews" when we have an inward circumcision.
For he is not a Jew, which is one outwardly; neither is that circumcision, which is outward in the flesh: But he is a Jew, which is one inwardly; and circumcision is that of the heart, in the spirit, and not in the letter; whose praise is not of men, but of God.
- Romans 2:28-29 (KJV)
This change surprised the apostles as well.
While Peter yet spake these words, the Holy Ghost fell on all them which heard the word. And they of the circumcision which believed were astonished, as many as came with Peter, because that on the Gentiles also was poured out the gift of the Holy Ghost. For they heard them speak with tongues, and magnify God. Then answered Peter,
- Acts 10:44-46 (KJV)
A great example of where we go from physical to spiritual is how in Christ we are of the seed of Abraham.
There is neither Jew nor Greek, there is neither bond nor free, there is neither male nor female: for ye are all one in Christ Jesus. And if ye be Christ's, then are ye Abraham's seed, and heirs according to the promise.
- Galatians 3:28-29 (KJV)
The process of adding the Gentiles to Israel is sometimes called "grafted in".
The phrase "grafted in" means "A shoot or bud of one plant that is inserted into or joined to the stem, branch, or root of another plant so that the two grow together as a single plant".
Paul speaks about this process as well:
For I speak to you Gentiles, inasmuch as I am the apostle of the Gentiles, I magnify mine office: If by any means I may provoke to emulation them which are my flesh, and might save some of them. For if the casting away of them be the reconciling of the world, what shall the receiving of them be, but life from the dead? For if the firstfruit be holy, the lump is also holy: and if the root be holy, so are the branches. And if some of the branches be broken off, and thou, being a wild olive tree, wert graffed in among them, and with them partakest of the root and fatness of the olive tree; Boast not against the branches. But if thou boast, thou bearest not the root, but the root thee. Thou wilt say then, The branches were broken off, that I might be graffed in. Well; because of unbelief they were broken off, and thou standest by faith. Be not highminded, but fear: For if God spared not the natural branches, take heed lest he also spare not thee. Behold therefore the goodness and severity of God: on them which fell, severity; but toward thee, goodness, if thou continue in his goodness: otherwise thou also shalt be cut off. And they also, if they abide not still in unbelief, shall be graffed in: for God is able to graff them in again. For if thou wert cut out of the olive tree which is wild by nature, and wert graffed contrary to nature into a good olive tree: how much more shall these, which be the natural branches, be graffed into their own olive tree?
- Romans 11:13-24 (KJV)
So yeah, we are spiritual Israel.