>>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"
What are the ‘terms’ of the covenant? In every covenant there are two parties to that covenant. What is required on our part and what was required on His. He has fulfilled in part what is required of Him, however, the question you did not answer is, what is required of us?