The Old Covenant was a bilateral covenant of which Yahveh and the nation of Israel were parties. The Israelites had to agree to the terms of the covenant, which they did (Exo. 24:7).
Is the New Covenant a bilateral covenant?
Yes, it is a bilateral covenant! This is the new covenant, Jeremiah 31:31-34 (NIV) :
“The days are coming,” declares the Lord, “when I will make a new covenant with the people of Israel and with the people of Judah. It will not be like the covenant I made with their ancestors when I took them by the hand to lead them out of Egypt, because they broke my covenant, though I was a husband to them,” declares the Lord. “This is the covenant I will make with the people of Israel after that time,” declares the Lord. “I will put my law in their minds and write it on their hearts. I will be their God, and they will be my people. No longer will they teach their neighbor, or say to one another, ‘Know the Lord,’ because they will all know me, from the least of them to the greatest,” declares the Lord. “For I will forgive their wickedness and will remember their sins no more.”
This new covenant started when Jesus poured out his blood (symbolized by the wine in the last supper), Luke 22:20 (NIV):
In the same way, after the supper he took the cup, saying, “This cup is the new covenant in my blood, which is poured out for you.
All we have to do to accept this new covenant is stated in Romans 10:9-12 (NIV):
If you declare with your mouth, “Jesus is Lord,” and believe in your heart that God raised him from the dead, you will be saved. For it is with your heart that you believe and are justified, and it is with your mouth that you profess your faith and are saved. As Scripture says, “Anyone who believes in him will never be put to shame.” For there is no difference between Jew and Gentile—the same Lord is Lord of all and richly blesses all who call on him, for, “Everyone who calls on the name of the Lord will be saved.”
Jesus basically stated the "terms" in John 15:5-7 (NIV), though not speaking specifically about a covenant:
“I am the vine; you are the branches. If you remain in me and I in you, you will bear much fruit; apart from me you can do nothing. If you do not remain in me, you are like a branch that is thrown away and withers; such branches are picked up, thrown into the fire and burned. If you remain in me and my words remain in you, ask whatever you wish, and it will be done for you.
Yes, the New Covenant is a bilateral covenant, and Dan the Man covers many of the salient points. I would also like to add a few points from the book of Hebrews, which gives a beautiful and in-depth description of how the New Covenant is so much better than the Old Covenant (Starting in Heb 7:11 and running through the end of chapter 10).
But first, here's how I'm using the terminology. A covenant is an agreement between two or more parties (basically a contract--verbal, written, or otherwise). A bilateral covenant is the kind we're most accustomed to, where both parties are expected to consent to the agreement before the agreement comes to life and is seen as valid and enforceable. That is, unless and until both parties agree to abide by the covenant/contract, there is no covenant/contract. A unilateral covenant is an agreement where one party agrees to do something regardless of the approval, interest, commitment, compliance, or participation of the other parties. There is still a commitment and contract being made. One party is still obligated to follow through on everything in the covenant. However, the responsibility to follow through is not dependent on the participation or behavior of the other party(ies). This would be like a man on his wedding day saying to his bride, "I promise to love you, for better or for worse, all the days of our lives." His promise is unilateral, and does not depend in any way on the performance or acceptance of his bride.
So in Heb 7:23-25, the writer says,
The former priests were many in number, because they were prevented by death from continuing in office, but he holds his priesthood permanently, because he continues forever. Consequently, he is able to save to the uttermost those who draw near to God through him, since he always lives to make intercession for them.
Here we see that salvation is not strictly unilateral. It doesn't take effect unless/until we draw near to God through Jesus. Again, it's not the difficulty or effort involved that makes a covenant or contract bilateral. If there is any requirement on the other party to do anything at all for that covenant or contract to go into effect or to stay in effect, then it is not unilateral.
"But wait," you might say, "the author here is talking about salvation...he hasn't said anything about the New Covenant per se." The writer is indeed speaking of the New Covenant here, and it will become clear over the next couple of chapters. Up till this point in Hebrews, the writer has been laying the groundwork of how much more excellent Jesus is than the earthly priesthood that had preceded him, and now he's going to show this even further, in the context of how much better the New Covenant is than the Old Covenant.
In Hebrews 8:7-13, the writer makes the definite tie-in between the New Covenant and the Old Covenant, saying:
For if that first covenant had been faultless, there would have been no occasion to look for a second.
For he finds fault with them when he says:
“Behold, the days are coming, declares the Lord, when I will establish a new covenant with the house of Israel and with the house of Judah, not like the covenant that I made with their fathers on the day when I took them by the hand to bring them out of the land of Egypt. For they did not continue in my covenant, and so I showed no concern for them, declares the Lord. For this is the covenant that I will make with the house of Israel after those days, declares the Lord: I will put my laws into their minds, and write them on their hearts, and I will be their God, and they shall be my people. And they shall not teach, each one his neighbor and each one his brother, saying, ‘Know the Lord,’ for they shall all know me, from the least of them to the greatest. For I will be merciful toward their iniquities, and I will remember their sins no more.”
In speaking of a new covenant, he makes the first one obsolete. And what is becoming obsolete and growing old is ready to vanish away.
Here the writer of Hebrews is making direct reference to the Jeremiah 31:31-34 where the Lord foretells the future coming of the New Covenant. And after continuing his comparison of the New and Old Covenants in chapter 9, the writer says in Heb 10: 19-31,
Therefore, brothers, since we have confidence to enter the holy places by the blood of Jesus, by the new and living way that he opened for us through the curtain, that is, through his flesh, and since we have a great priest over the house of God, let us draw near with a true heart in full assurance of faith, with our hearts sprinkled clean from an evil conscience and our bodies washed with pure water. Let us hold fast the confession of our hope without wavering, for he who promised is faithful. And let us consider how to stir up one another to love and good works, not neglecting to meet together, as is the habit of some, but encouraging one another, and all the more as you see the Day drawing near.
For if we go on sinning deliberately after receiving the knowledge of the truth, there no longer remains a sacrifice for sins, but a fearful expectation of judgment, and a fury of fire that will consume the adversaries. Anyone who has set aside the law of Moses dies without mercy on the evidence of two or three witnesses. How much worse punishment, do you think, will be deserved by the one who has trampled underfoot the Son of God, and has profaned the blood of the covenant by which he was sanctified, and has outraged the Spirit of grace? For we know him who said, “Vengeance is mine; I will repay.” And again, “The Lord will judge his people.” It is a fearful thing to fall into the hands of the living God.
Now at this point, some might say, "Hey wait a minute, wasn't the book of Hebrews written to Jews? Does this all really apply to me?" Well yes, it was written to Jews. It was written to Jews who had chosen to believe in Jesus, but who were struggling with their connection to the Old Covenant and what it now meant to be a Jew and a follower of Jesus. The ultimate question for these Jews was where the Old Covenant, Moses, all the Jewish traditions, and their now-tenuous connection to the Jewish community all fit in with life in Christ. So the writer of Hebrews was saying to them, "Look brothers, you formerly trusted in the old sacrificial system to cover your sins, but that's no longer available. So now, having heard that the only way for your sins to be cleansed is through Jesus, you really must come to him! Because if you don't, you have nothing to rely on under the Old Covenant anymore. Fellow Jew, don't be tempted to leave your trust in Jesus and return to the Old Covenant! It's kaput. It's done. Unless you come to Jesus and stay, your only future expectation is a fiery judgment."
So it was necessary for the Jew to "do something" in order to enter into the New Covenant. First, he had to willingly leave his place of reliance on the Old Covenant. And then, he had to place that trust and reliance solely upon Jesus. And it's no different for the Gentile. We all are inaugurated into the New Covenant in the same fashion. We must leave our trust and reliance upon anything else for our righteousness, and place that hope firmly and solely in Jesus.
So the New Covenant is bilateral. Our part is to come to Jesus, and to trust in him completely. The New Covenant is truly beautiful, truly powerful, and truly better than the Old Covenant it replaced. The New Covenant works (where the Old failed) because there is so much less for us to do, and so much more for God to do. In fact, if it weren't for the "coming" and "trusting" part, the New Covenant would be completely unilateral. We simply come to Jesus and trust him fully, and in doing so, he changes us completely and comes to dwell within us. This is what makes the New Covenant work--Christ in us, because where the Old Covenant was lived out by man's power and resources to obey, the New Covenant is lived out by Jesus' power and resources to obey. The New Covenant is so much better because Jesus is perfect, and because under this New Covenant it is no longer I who lives, but Christ lives in me, and this I do by faith in the Son of God, who loved me and gave himself for me!
The First Covenant is unilateral:
When the sun had set and darkness had fallen, a smoking firepot with a blazing torch appeared and passed between the pieces. On that day the Lord made a covenant with Abram.... Genesis 15: 17-18a
My understanding on this point comes from a sermon by Tullian Tchvidjian, but I have found similar explanation of contract covenants at the time:
A Chaldean custom for the confirmation of a covenant or contract was for the covenanting parties to slay an animal, split it, and then walk between the two halves. The thought behind the custom seems to have been that the fate of the slain animal should be also the fate of the one who would break the covenant or contract
But in our story, we only see one party-- the smoking firepot representing God-- doing the walking. Paul confirms this (see also Romans 11):
For if the inheritance is of the law, it is no more of promise: but God hath granted it to Abraham by promise. Galatians 3:18
The Second Covenant is unilateral:
But God demonstrates his own love for us in this: While we were still sinners, Christ died for us. Romans 5:8
From a sole fide or sola gratia perspective, the New Covenant is inherently unilateral.
Probably the most famous verse on grace - Ephesians 2:8-9, states it explicitly:
For by grace, you are saved through faith. It is not through any work of your own lest any man should boast.
A bi-lateral covenant would entail work on the other party. Grace (meaning "Gift") explictly rejects that. To say otherwise to someone who values grace tells me that a child receiving a christmas present has likewise entered into a bilateral covenant. Try telling my kid that.
God's covenant's are neither unilateral nor bilateral, but they are colateral, meaning that even though Jesus" has been made a propitiation for us and taken the anger of God on our behalf and is the mediator of the new covenant, The covenant itself, set up by God himself to reconcile his creation, man, male and female, back to himself, this covenant is made solely by and offered to us by God, it is his covenant, made in Jesus' blood, but we must accept that covenant or not accept it, therefore we must enter into it and agree upon the conditions of the covenant God offers to us by faith in His Son, so this is a colateral covenant that requires both sides to believe in and abide by the covenant. Jesus, the mediator of the covenant offers to each person as a free gift but they must receive it by faith. Jesus said , if, which is conditional, you abide in me and my word abides in you, and those that have the spirit of Christ abiding in them they are his. We must do our part and abide in Him as he has stated in his word and continue in Him by faith. It is a colateral covenant which is dependent on both parties doing their part in the honoring of the covenant.