H/T Nathan White.
There are clear passages indicating that ‘the forgiveness of sins’ is unique to the New Covenant (“remember their sins no more”; Jer 31:34). This is not because OT saints were under God’s wrath but because God overlooked their sins; he covered them over through the sacrificial system. This I take to be Paul’s point in Romans 3:25 (ESV), referring to Christ “whom God put forward as a propitiation by his blood, to be received by faith. This was to show God’s righteousness, because in his divine forbearance he had passed over former sins.” They were forgiven truly but only by anticipation and were not yet propitiated in history. The old covenant was successful only to the extent that it directed faith and hope toward Christ, but it could not in itself bring this reality into history. These sacrifices could never “take away sins” once and for all. They had to be offered repeatedly, reminding the worshiper’s conscience of transgressions (Heb 10:1-4). “But when Christ had offered for all time a single sacrifice for sins, he sat down at the right hand of God, waiting from that time until his enemies should be made a footstool for his feet. For by a single offering he has perfected for all time those who are being sanctified” (vv. 12-14). From there, the writer quotes Jeremiah 31:33, which I have cited above, linking forgiveness and the gift of the Spirit.
If this is accurate, then Old Testament believers were forgiven and justified through faith in the one to whom the sacrifices pointed (continuity); however, the sacrifices could not themselves provide this experiential assurance to the conscience (discontinuity). On the contrary, the Mosaic covenant by itself could only keep the covenant people under supervision until they reached their maturity and could inherit the estate by promise (Gal 3:24-25). Kuyper seems to confirm this conclusion. He argued that the energies of the Spirit at Pentecost worked retroactively in the lives of OT saints.