(This is a copy of a response to an astute question raised in the comment section of the previous post. It seeks to show how the same good God worked out a single plan from OT promise to NT fulfillment.)
The OT on its own terms presents a story that is headed somewhere yet is incomplete and pointing forward. The NT presents Jesus as the completion to the story.
The direction in which the OT story is heading is God ruling over a perfected world, with a perfected people living in right relationship with him (see Gen 1:26-30 and Gen 2 for a glimpse of this end goal). The Israelites received the first taste of this perfected rule and loving relationship through the covenants God made with them (and God promised blessing to all nations through Israel – Gen 12:1-3). But because of deep-rooted sin (towards God and others) they fell short of experiencing God’s reign, and the relationship was broken, pending a new work of God (promised in Jer 31:31-34 and elsewhere).
Jesus comes as the faithful, sacrificial savior and vindicated, resurrected victor, both to provide for the sins of Jews and Gentiles (giving us relationship with God) and to inaugurate the reign of God (“the kingdom of God”). All of this will come to fruition when Christ returns.
In short, the “old method”/old covenant was a good part of God’s overarching plan that was fulfilled in Christ. This was the plan God always had in mind (2 Tim 1:9; Eph 1:9-10) and was even foreshadowed throughout the OT (see the entire book of Hebrews for examples). The shortcomings under the old covenant were related to human failure rather than deficiency of divine design (see Rom 7 for this argument from Paul).
That is a very simplistic overview of the OT and NT, but I hope it helps for starters!