Just some words from John Calvin on the covenants as I read through this article on Calvin’s view of the (ana)baptist position.

While such confirmation was awaited, the Lord appointed, through Moses, ceremonies that were, so to speak, solemn symbols of that confirmation. A controversy arose over whether or not the ceremonies that had been ordained in the law ought to give way to Christ. Now these were only the accidental properties of the covenant, or additions and appendages, and in common parlance, accessories of it. Yet because they were means of administering it, they bear the name “covenant,” just as is customary in the case of other sacraments. To sum up, then, in this passage “Old Testament” means the solemn manner of confirming the covenant, comprised in ceremonies and sacrifices. (II. 11. 4)

Or, if you prefer, understand it thus: the Old Testament of the Lord was that covenant wrapped up in the shadowy and ineffectual observance of ceremonies and delivered to the Jews; it was temporary because it remained, as it were, in suspense until it might rest upon a firm and substantial confirmation. It became new and eternal only after it was consecrated and established by the blood of Christ. Hence Christ in the supper calls the cup that he gives to his disciples, “the cup of the New Testament in my blood.” By this he means that the Testament of God attained its truth when sealed by his blood, and thereby becomes new and eternal. (II. 11. 4)