14But Peter, standing with the eleven, lifted up his voice and addressed them: "Men of Judea and all who dwell in Jerusalem, let this be known to you, and give ear to my words. 15For these people are not drunk, as you suppose, since it is only the third hour of the day. 16But this is what was uttered through the prophet Joel:
17 "'And in the last days it shall be, God declares, that I will pour out my Spirit on all flesh,and your sons and your daughters shall prophesy,
and your young men shall see visions,
and your old men shall dream dreams;
18even on my male servants and female servants
in those days I will pour out my Spirit, and they shall prophesy.
19And I will show wonders in the heavens above
and signs on the earth below,
blood, and fire, and vapor of smoke;
20 the sun shall be turned to darkness
and the moon to blood,
before the day of the Lord comes, the great and magnificent day.
21And it shall come to pass that everyone who calls upon the name of the Lord shall be saved.'
There are some important things about this passage to notice.
Firstly Peter is addressing "men of Judea" and all who dwell in Jerusalem, later he addresses "men of Israel". Peter's sermon is specifically directed toward the Jews and Jewish converts in the audience. Peter, at this point, doesn't have Gentiles in view or recognize that the promise of salvation extends to them outside of Judaism. While it is true that Peter is quoting Joel, the context is strictly within the boundaries of Israel, thus the quote is covenantal in scope. Notice what the quote says:
your sons and your daughters shall prophesy...
your young men shall see visions...
your old men shall dream dreams...
even on my male servants and female servants...
The actual passage in Joel says "your male servants...", the context here is federal household relationship within the covenant of Abraham. There is simply no way that Peter, a devout Jew would be dichotomizing the covenant, or even foreseeing a divergence therein.
Paul, in expressing dismay at the people of Galatia who are seeking circumcision to be included with in the covenant of Abraham, states something astounding:
Gal 3:14 so that in Christ Jesus the blessing of Abraham might come to the Gentiles, so that we might receive the promised Spirit through faith.
It seems that Paul sees the promise of the Spirit and the blessing of Abraham as one and the same. This makes perfect sense given Paul's theme of a contrast between the offspring of the flesh and those of the Spirit. (Rom 8, 9, 10, Gal 3-5, et al) Thus Paul does not see the New Covenant as a completely new covenant, never before seen, not having anything to do with the promise of the Spirit, but rather a fulfillment and continuum of the covenant of promise made with Abraham.
This is why Paul states that Gentile believers are in fact Abraham's true offspring and thus inheritors of the promises of that covenant. He doesn't say that they're part of a different covenant, but the one same covenant made with Abraham. The New Covenant therefore cannot be completely new, in the sense that Reformed Baptists mean it, but rather a new administration of that one covenant of grace made with Abraham, with new rites, signs and seals.