How is the covenant of grace administered under the New Testament?

Under the New Testament, when Christ the substance was exhibited, the same covenant of grace was and still is to be administered in the preaching of the word,[1] and the administration of the sacraments of Baptism [2] and the Lord's Supper;[3] in which grace and salvation are held forth in more fulness, evidence, and efficacy, to all nations.[4]

1. Mark 16:15

   And he said to them, “Go into all the world and proclaim the gospel to the whole creation.

   
   
2. Matt. 28:19-20

   Go therefore and make disciples of all nations, baptizing them in the name of the Father and of the Son and of the Holy Spirit, teaching them to observe all that I have commanded you. And behold, I am with you always, to the end of the age.

   
   
3. I Cor. 11:23-25

   For I received from the Lord what I also delivered to you, that the Lord Jesus on the night when he was betrayed took bread, and when he had given thanks, he broke it, and said, “This is my body which is for you. Do this in remembrance of me.” In the same way also he took the cup, after supper, saying, “This cup is the new covenant in my blood. Do this, as often as you drink it, in remembrance of me.”

   
   
4. II Cor. 3:6-9

   ....who has made us competent to be ministers of a new covenant, not of the letter but of the Spirit. For the letter kills, but the Spirit gives life.
   
   Now if the ministry of death, carved in letters on stone, came with such glory that the Israelites could not gaze at Moses' face because of its glory, which was being brought to an end, will not the ministry of the Spirit have even more glory? For if there was glory in the ministry of condemnation, the ministry of righteousness must far exceed it in glory.

   
   Heb. 8:6, 10-11

   But as it is, Christ has obtained a ministry that is as much more excellent than the old as the covenant he mediates is better, since it is enacted on better promises....
   
   For this is the covenant that I will make with the house of Israel
   after those days, declares the Lord:
   I will put my laws into their minds,
   and write them on their hearts,
   and I will be their God,
   and they shall be my people.
   And they shall not teach, each one his neighbor
   and each one his brother, saying, ‘Know the Lord,’
   for they shall all know me,
   from the least of them to the greatest.

   Matt. 28:19 (See above.)
   

Question 35, Westminster Larger Catechism.

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