That the New Covenant is applied to the Church of the Gospel age, and will also be applied to the people in the Kingdom age, is perfectly plain from a consideration of the specifications of the New Covenant as referred to in various Scriptures.
“I will put my laws into their mind, and write them in their hearts.” (Heb. 8 : 10.)
” I will be to them a God, and they shall be to Me a people.” (Heb. 8: 10.)
“They shall not teach every man his neighbour and every man his brother, saying, Know the Lord; for all shall know Me from the least to the greatest.” (Heb. 8: 11.)
is what Jehovah God said, because God found fault with the people.
“For I will be merciful to their unrighteousness, and their sins and their iniquities will I remember no more.” (Heb. 8: 12.)
27 For this is my covenant unto them, when I shall take away their sins.
28 As concerning the gospel, they are enemies for your sakes: but as touching the election, they are beloved for the father’s sakes.
29 For the gifts and calling of God are without repentance.
30 For as ye in times past have not believed God, yet have now obtained mercy through their unbelief:
31 Even so have these also now not believed, that through your mercy they also may obtain mercy.
32 For God hath concluded them all in unbelief, that he might have mercy upon all. (Romans 11:27-32 KJV)