God gradually unfolds before us what the conditions for conversion are. Layer upon layer of truth, or revelation, is needed to get the fullness of a subject.
Here are the conditions: We have to be called (John 6:44). We have to repent. We have to believe the gospel. We have to believe in Jesus Christ. We have to begin obeying God, because God gives His Spirit to those who obey Him (John 14:15-18; Acts 5:32). We have to be baptized in the name of Jesus Christ. We also have to have hands laid on us (Acts 8:14-17).
This should help us to understand that the "writing of the law on our hearts" (Hebrews 8:10) is a cooperative effort. It is not something done only by God, but it absolutely requires what God does. It also requires that we do something. When a person does these things, he is meeting the terms of the New Covenant - not all of them yet.
Were there terms like this in the Old Covenant? No. What a difference exists between the two! It is no wonder that the Old Covenant is becoming obsolete (Hebrews 8:13). It is no wonder the Old Covenant could not be kept (Hebrews 8:7). There is such a flaw, a fault, in every one of us (Hebrews 8:8). God knew this when He made the Old Covenant with Israel. Since God is love, He left us an example of how much the New Covenant means to us, so that we could look back on history and understand what awesome gifts have been given to us. By that, He hopes to create within us a deep sense of thanksgiving and of obligation.