Greetings in that Divine and Most Precious Name of Our Lord and Savior Jesus Christ!
The Apostle Paul didn't necessarily say the Church is the new Israel, rather in Galatians chapter 6 the Church is referred to as
And as many as walk according to this rule, peace and mercy be upon them, and upon the Israel of God.
Here is what Saint John Chrysostom
had to say about it
This our rule of life he calls “a new creature,” both on account of what is past, and of what is to come; of what is past, because our soul, which had grown old with the oldness of sin, hath been all at once renewed by baptism, as if it had been created again.163 Wherefore we require a new and heavenly rule of life. And of things to come, because both the heaven and the earth, and all the creation, shall with our bodies be translated into incorruption. Tell me not then, he says, of circumcision, which now availeth nothing; (for how shall it appear, when all things have undergone such a change?) but seek the new things of grace. For they who pursue these things shall enjoy peace and amity, and may properly be called by the name of “Israel.” While they who hold contrary sentiments, although they be descended from him (Israel) and bear his appellation, have yet fallen away from all these things, both the relationship and the name itself. But it is in their power to be true Israelites, who keep this rule, who desist from the old ways, and follow after grace.