Hyperdispensationalism.
Gospel was given to Paul? Christ gave it to Abraham, and, according to Gal 3 and Rom 4, it was salvation by faith alone. Especially Gal 3 emphasizes that even Mosaic law did not interrupt the ongoing Abrahamic covenant of faith.
Examples that the gospel is nothing new (because the cross is retroactive to all OT saints):
"Understand, then, that those who have faith are children of Abraham.
8Scripture foresaw that God would justify the Gentiles by faith, and
announced the gospel in advance to Abraham: “All nations will be blessed through you.”
d 9So those who rely on faith are blessed along with Abraham, the man of faith" (Gal 3)
"For unto us was the gospel preached,
as well as unto them" (Heb 4:2)
Salvation has never been by good works. It is by the cross. This means that OT and NT saints - since they both get the same cross - HAD to operate under the same dispensation of grace, the same Covenant.
Peter? In the Book of Acts neither Peter nor anyone else has much to say about a New Covenant. Your words seem to be a theological construct fabricated by your own theological presuppositions. I don't see much basis for concluding that your position is a fact of Scripture.
The Book of Acts DOES mention the ongoing Abrahamic Promise/Covenant, as I seem to recall.