Was There a '7' Associated With the New Covenant? I have heard from several places that Covenant making often involves the number 7 in some way. I don't ever recall a mentioning of a 7 associated with Jesus institution of the Eucharist and his death and Resurrection. Is there a '7' to be found somewhere in Jesus sacrifice or is Jesus use of the words 'Covenant' in the institution narrative make a '7' unnecessary?
We do know that the sabbath happens on the seventh day. It is also the case that the Hebrew word for seven stands not only for a number. Sheba is also a verb, “and it means to swear a covenant oath – literally to ‘seven oneself"


  see. Genesis 21:27-32


The sabbath is not so much a day for the Father to rest, but stands as a sign of the covenant God made with creation.  “The sabbath symbolized man’s God-given destiny: to rest in God’s blessing and holiness for all eternity” 

So the number seven is an "covenant oath". When making covenant oaths the lord would also establish outward signs of that covenant oath.  Christ is his earthly Minestry did the same.

The Seven sacraments of the Catholic Church according to Saint Augustine are


  outward signs of invisible Graces


These graces, given to the Church by our lord and savior, are covenant oaths, signs of the new covenant.  

For more information check here:

http://rcdow.org.uk/att/files/faith/catechesis/baptism/sacraments.pdf

There is indeed a "7" accociated with the new Covenant, they are the Seven Sacrements of the Catholic Church.