Turretin grants that there were differences in the administration of the covenant of grace in the Old Testament and the New but that it was the same in substance and essential parts. The issue is one of continuity of content:
Here are some extracts from his exposition and defence of the unity of the covenant of grace:
Whether the same Mediator (Christ) in both; the same faith in Christ; promises of the same spiritual and heavenly blessings; the same way of reconciliation and salvation—the economy and administration only of the covenant varying. This our opponents deny; we affirm. (5th Q: V)
The question is not whether the fathers of the Old Testament were saved, whether their sins were pardoned, whether they had any hope of eternal life, whether Christ was predicted to them. Most of our adversaries do not dare to deny this. Rather the question is whether they looked to Christ and were saved in the hope of his coming. Whether promises not only temporal, but also spiritual and heavenly concerning eternal life and the Holy Spirit were given to them. And whether the same covenant entered into with us in Christ had already been contracted with them, although more obscurely and reservedly.
We maintain that Christ was not only predicted but also promised to the fathers and by his grace they were saved under the Old Testament no less than we are saved under the New; nor was any name given under heaven from which salvation could be hoped for (Acts 4:12) and that too according to the inviolable promise of the gratuitous covenant. (5th Q: VI)
It is also falsely alleged that the words “There is none other name under heaven given among men, whereby we must be saved” (Acts 4:12) refer only to the time in which Christ was manifested and cannot be extended to the past.
...since no salvation can be granted to the sinner without a mediator (and there is no mediator except Christ), it follows either that the fathers had no salvation or that they were saved by Christ. (5th Q: XII)
Peter testifies, “To Christ give all the prophets witness, that through his name whosoever believeth in him shall receive remission of sins” (Acts 10:43). Nor can it be objected that the faith of the ancients was general in God, not special in Christ (the Saviour), because the opposite is evident from many considerations.
(a) No faith can be saving unless founded upon Christ.
(b) He speaks of the faith by which they looked to God as their God (Heb. 11:16) and to heaven as their native country. Now this cannot be done without Christ.
(c) Of the faith by which they looked to Christ himself and preferred his reproach to all treasures (Heb. 11:26). (d) Not only a general but also a special command of faith in Christ is found in the Old Testament (Exod. 23:20-21; Deut. 18:18; Ps. 2:12; Is. 53:1, 5). If the faith of the ancients were not the same as ours, it would be improperly proposed for our imitation (Heb. 12:1, 2; Rom. 4:12). Paul could not argue with sufficient strength from the faith of the father of believers and his justification to ours (Gal. 3:6, 7; Rom. 4:16). (5th Q: XIV)
It cannot be objected:
(1) as to the promises concerning Christ in the Old Testament that they were indeed given to the fathers, but not for the fathers; rather for the believers of the New Testament, as the promises of the calling of the Gentiles were given to the ancients, but only for the time of the New Testament.
(a) It is absurd that the prophets should have given such promises to believers and that believers heard them and did not apply them to themselves. For they were oppressed by the same evils as others for whom they are supposed to have been made and equally in need of the same remedy. Since they were sent to the ancient people in order to sustain them in the hope of the Messiah about to come and of the salvation to be obtained through him, who does not see that such promises were given to the fathers for their consolation?(b) The promises belonged to them in the same manner as the adoption, glory, the covenants, the giving of the law and the service of God (Rom. 9:4)
(c) If the promises did not pertain to them, they could not and ought not to have applied them to themselves, as was done by Abraham (Gen. 15:6), who also was justified in this way (Rom. 4:4); by Jacob (Gen. 49:18); by David (Pss. 16, 23, 40, 110, 118 and frequently elsewhere); by Isaiah (Is. 9:6-- “Unto us a child is born, unto us a son is given”) and by the whole Israelite church (Is. 53:11). (5th Q: XVI)