score:1
To my understanding, covenant theology is a lens through which to interpret scripture and understand it. It appears from the answer below that this way of interpreting and understanding scripture encompasses the traditionally understood purpose behind Jesus' death with the institution of the New Covenant [NT].
What is Covenant Theology in Reformed Theology?
Covenant theology (also known as Covenantalism, Federal theology, or Federalism) is a Calvinist conceptual overview and interpretive framework for understanding the overall flow of the Bible. It uses the theological concept of covenant as an organizing principle for Christian theology. The standard description of covenant theology views the history of God's dealings with mankind, from Creation to Fall to Redemption to Consummation, under the framework of the three overarching theological covenants of redemption, works, and grace.1
1. cf. Covenant Theology | Wikipedia.
Repeating, the three overarching theological covenants are:
This is in contrast to the [Catholic] Perspective of the Old Covenant and the New and Everlasting Covenant (Old Testament and New Testament).
The covenant that appears to answer the questions - How does Reformed theology in particular connect its view of the purpose behind Jesus' death with the institution of the New Covenant? Or does Reformed theology talk much about the New Covenant? What sort of emphasis does it place on any connection between the Covenant and the Sacrifice? - is the covenant of grace, the promised eternal blessing for belief in Christ and obedience to God's word. It is seen as the basis for all biblical covenants that God made individually with Noah, Abraham, and David, nationally with O.T. Israel as a people, and universally with man in the New Covenant (sic).2
2. cf. Covenant of Grace | Theopedia.
Thus from my rudimentary understanding, the covenants of works is that pre-Fall agreement between God and Adam in which Adam was promised blessing and life upon obedience to the terms of the covenant and cursing and death should he disobey the terms of the covenant. The covenant of grace as above, and both founded on the covenant of redemption.
Further reading: