The Old Testament presents itself, then, as a story that is headed somewhere. The Old Testament closes with both anxiety and hope under Persian rule (see Malachi). The books of the Second Temple Period (between the Old and New Testaments) continue this notion of God’s people chosen for a purpose, but not all strands of this material make clear what that purpose is. Some of these Second Temple books offer endings for the story (e.g., in the Qumran community as the elect), but the faithful were looking for more. . .The New Testament authors, most of whom were Jewish Christians, saw themselves as heirs of the Old Testament story and as authorized to describe its proper completion in the death and resurrection of Jesus and the messianic era that this ushered in. These authors appropriated the Old Testament as Christian Scripture, and they urged their audiences (many of whom were Gentile Christians) to do the same. There is debate over just how the New Testament authors used the Old Testament as Scripture. . .but the simplest summary of the New Testament authors’ stance would be to say that they saw the Old Testament as constituting the earlier chapters of the story in which Christians are now participating.
From: “The Theology of the Old Testament” by C. John Collins, in ESV Study Bible (English Standard Version) (Wheaton: Crossway, 2008), p. 31.