In his helpful summary of systematic theology called Our Reasonable Faith, Herman Bavinck defines the covenant of grace in a clear and concise way. He introduces this section with these words: “When we give our attention to this historical development of the covenant of grace, we detect a trio of remarkable characteristics in it.” What follows is my summary of Bavinck’s three part discussion. (Note: the term “dispensation” below doesn’t have anything to do with dispensationalism; it means more generally “age” or “epoch” or “divine arrangement” in line with the later Medieval Latin use.)
“In the first place, the covenant of grace is everywhere and at all times one in essence, but always manifests itself in new forms and goes through differing dispensations. Essentially and materially it remains one, whether before, or under, or after the law. It is always a covenant of grace. It is called this because it issues from the grace of God, has grace as its content, and has its final purpose in the glorification of God’s grace. We have to note particularly therefore that this promise (I will be your God and the God of your people) is not conditional, but is as positive and certain as anything can be. God does not say he ‘will’ be our God ‘if’ we do this or that. He says rather that he will put enmity, that he will be our God, that in Christ he will grant us all things. The covenant of grace can throughout the centuries remain the same because it depends entirely upon God and because God is the immutable One and the faithful One.”
“The second remarkable characteristic of the covenant of grace is that in all of its dispensations it has an organic character. In history the covenant is never concluded with one discrete individual, but always with a man and his family or generation, with Adam, Noah, Abraham, Israel, and with the church and its seed. The promise never comes to a single believer alone, but in him his house or family also. God does not actualize his covenant of grace by picking a few people out of humanity at random, and by gathering these together into some sort of assemblage alongside the world. Rather he bears his covenant into mankind, makes it part and parcel of the world, and sees to it that in the world it is preserved from evil. Grace is not a legacy which is transferred by natural birth, but it does flow on in the river-bed which has been dug out in the natural relationships of the human race. The covenant of grace does not ramble about at random, but perpetuates itself, historically and organically, in families, generations, nations.”
A third and final characteristic of the covenant of grace which goes along with the second point above, is that it realizes itself in a way which fully honors man’s rational and moral nature. It is based on the counsel of God, yes, and nothing may be subtracted from that fact. Behind the covenant of grace lies the sovereign and omnipotent will of God. But God’s will is the will of the Creator of heaven and earth, who cannot repudiate his own work in creation or providence, and who cannot treat the human being he has created as though it were a stock or stone. It is the will of a merciful and kind Father, who never forces things with brute violence, but successfully counters all our resistance by the spiritual might of love. The will of God realizes itself in no other way than through our reason and our will. That is why it is rightly said that a person, by the grace he receives, himself believes and himself terms from sin to God.”
Bavinck does reference quite a few Scripture texts above; one will have to read his full discussion to see how he grounds his explanations in Scripture. The entire section is found on pages 274-278 of Our Reasonable Faith (Grand Rapids, Baker, 1956).