What role does the New Covenant play in Reformed Theology? After looking at @Affable Geek's answer to an overview question on different understandings of why Jesus had to die, and in particular after his comment on Catholicism in this respect, I went to look at the discussion in the Catechism of the Catholic Church regarding the role of the death of Jesus in salvation. .
One thing that struck me about the Catechism's discussion of &quot;Why did Jesus die?&quot; is the intimate connection the Catechism draws between the offering of Jesus on the Cross and the institution of the New Covenant. This connection is evident in the language of paragraph 610,

On the eve of his Passion, while still free, Jesus transformed this Last Supper with the apostles into the memorial of his voluntary offering to the Father for the salvation of men: &quot;This is my body which is given for you.&quot; &quot;This is my blood of the covenant, which is poured out for many for the forgiveness of sins.&quot;

and also in the language of the Eucharistic Prayer:

When supper was ended,
he took the chalice1 and, once more giving thanks,
he gave it to his disciples, saying:
Take this, all of you, and drink from it:
for this is the chalice of my Blood,
the Blood of the new and eternal covenant,
which will be poured out for you and for many
for the forgiveness of sins.

That is, rather than specifying a single reason why Jesus had to die (was it as a ransom from sin? an atonement for humanity?), Catholicism appears to focus instead on the New Covenant between God and Man which His death and resurrection created.
I don't see this connection being made in the soteriological approaches discussed in the answer above. 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 not talk much about the New Covenant? What sort of emphasis does it place on any connection between the Covenant and the Sacrifice?

1 There are a number of difficulties I have with the new translation of the Roman Missal; one is the translation of &quot;calix&quot; as &quot;chalice&quot; rather than the simple &quot;cup&quot; of the previous translation.
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:


The covenant of works, 
The covenant of redemption, and 
The covenant of grace.


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:


What Is Covenant Theology?.
The Doctrine of the Covenant in Reformed Theology by Geerhardus Vos.
Covenant Theology 4: The Covenant of Redemption By Carl Gobelman.