>>what is this "new covenant" with the "church" you speak of?
It's the forgiveness of sin through the sacrifice of Jesus Christ.
He is the lamb of the new covenant - perfect and sinless - He took the debt for our sins upon himself.
Luke 22:20
20 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."
NIV
Heb 9:15
15 For this reason Christ is the mediator of a new covenant, that those who are called may receive the promised eternal inheritance now that he has died as a ransom to set them free from the sins committed under the first covenant.
NIV
"Christ Frees Us"