When instituting the Lord's Supper, Jesus Christ said ([Luke 22:20](https://www.biblegateway.com/passage/?search=Luke+22%3A20&version=NIV), NIV):

> In the same way, after the supper he took the cup, saying, “This cup
> is the new covenant in my blood, which is poured out for you.

 
And in [Jeremiah 31](https://www.biblegateway.com/passage/?search=jeremiah+31&version=NIV) the new covenant is also mentioned, with the blessings of the covenant listed.  [Hebrews 8](https://www.biblegateway.com/passage/?search=hebrews+8&version=NIV) talks about the new covenant superceding the old in some way (the details of which perhaps I will put in another question). 

**At which stage did this new covenant supersede the older covenant, according to Reformed theology?**