Who foretold the New Covenant? How does it apply to the redemption?

Jeremiah 31:31 foretold it. Covenant condition was obedience, basically that of Jesus (Rom 5:19) to which His Mother's obedience was joined, not as adding - her whole ability came from Him, but as making things richer in good order (cf. Is 19:5.c., and LG 61).