If God's promises to Israel under the Old Covenant were conditional, and Israel broke the covenant, how then can God still fulfil His promises? What book, chapter, verse speaks to this please?
The promises of blessing and curses in the Old Covenant were conditional. For example, notice the language found in Leviticus 26:
Lev. 26:3 ‘If you walk in My statutes and keep My commandments so as to carry them out,
Lev. 26:4 then I shall give you rains in their season, so that the land will yield its produce and the trees of the field will bear their fruit.
Lev. 26:14 ‘But if you do not obey Me and do not carry out all these commandments,
Lev. 26:15 if, instead, you reject My statutes, and if your soul abhors My ordinances so as not to carry out all My commandments, and so break My covenant,
Lev. 26:16 I, in turn, will do this to you: I will appoint over you a sudden terror, consumption and fever that will waste away the eyes and cause the soul to pine away; also, you will sow your seed uselessly, for your enemies will eat it up.
Clearly, the blessings (and curses) found in the Old Covenant depended on Israel's obedience. If they obeyed, they would be blessed; disobey and be cursed. In this sense, the covenant is conditional.
Contrast that to the language of the Abrahamic covenant:
Gen. 12:1 Now the LORD said to Abram,
“Go forth from your country,
And from your relatives
And from your father’s house,
To the land which I will show you;
Gen. 12:2 And I will make you a great nation,
And I will bless you,
And make your name great;
And so you shall be a blessing;
Gen. 12:3 And I will bless those who bless you,
And the one who curses you I will curse.
And in you all the families of the earth will be blessed.”
The Lord made promises to Abraham without condition or requirement for obedience. This covenant (called a suzerainty covenant) is a grant of privilege without a requirement for obedience or even agreement on the part of the beneficiary. To demonstrate that the covenant had no requirements, the Lord physically immobilized Abraham during the establishment of the covenant:
Gen. 15:12 Now when the sun was going down, a deep sleep fell upon Abram; and behold, terror and great darkness fell upon him.
Gen. 15:13 God said to Abram, “Know for certain that your descendants will be strangers in a land that is not theirs, where they will be enslaved and oppressed four hundred years.
Gen. 15:14 “But I will also judge the nation whom they will serve, and afterward they will come out with many possessions.
Gen. 15:15 “As for you, you shall go to your fathers in peace; you will be buried at a good old age.
Gen. 15:16 “Then in the fourth generation they will return here, for the iniquity of the Amorite is not yet complete.”
Gen. 15:17 It came about when the sun had set, that it was very dark, and behold, there appeared a smoking oven and a flaming torch which passed between these pieces.
So the promises of the Old Covenant were conditional because they depended upon Israel's obedience to the Law, while the Abrahamic Covenant is unconditional since the fulfillment of the covenant solely depends on God's faithfulness to His word.
Despite their obvious differences, these two covenants work together to bring about all that God has promised to His people. Specifically, in Leviticus 26 (and elsewhere in the Law), the Lord connects the fulfillment of one covenant to the fulfillment of the other:
Lev. 26:40 ‘If they confess their iniquity and the iniquity of their forefathers, in their unfaithfulness which they committed against Me, and also in their acting with hostility against Me —
Lev. 26:41 I also was acting with hostility against them, to bring them into the land of their enemies — or if their uncircumcised heart becomes humbled so that they then make amends for their iniquity,
Lev. 26:42 then I will remember My covenant with Jacob, and I will remember also My covenant with Isaac, and My covenant with Abraham as well, and I will remember the land.
Lev. 26:43 ‘For the land will be abandoned by them, and will make up for its sabbaths while it is made desolate without them. They, meanwhile, will be making amends for their iniquity, because they rejected My ordinances and their soul abhorred My statutes.
Lev. 26:44 ‘Yet in spite of this, when they are in the land of their enemies, I will not reject them, nor will I so abhor them as to destroy them, breaking My covenant with them; for I am the LORD their God.
The Lord told Israel that despite receiving curses for failure to keep the Old Covenant, nevertheless the Lord would remain faithful to His people. The basis of the Lord's faithfulness to Israel was not the Old Covenant, but rather it was the Abrahamic Covenant. Since the Abrahamic Covenant was unconditional, the Lord was bound to preserve and protect Israel forever despite their failure to keep the Old Covenant.
So in Leviticus 26:40-42 the Lord promises to one day restore Israel to her land (i.e., to give her the Kingdom) when the nation confesses its sin in rejecting Jesus and places faith in the Messiah. That day is coming, and Zechariah say it happens at the end of Tribulation:
Zech. 12:9 “And in that day I will set about to destroy all the nations that come against Jerusalem.
Zech. 12:10 “I will pour out on the house of David and on the inhabitants of Jerusalem, the Spirit of grace and of supplication, so that they will look on Me whom they have pierced; and they will mourn for Him, as one mourns for an only son, and they will weep bitterly over Him like the bitter weeping over a firstborn.
Zech. 12:11 “In that day there will be great mourning in Jerusalem, like the mourning of Hadadrimmon in the plain of Megiddo.
At the end of Tribulation, the Lord pours out His Spirit on Israel leading the people of God to confess Christ ("the one whom they pierced") and by that confession they meet the terms of Leviticus 26:40-42. Once a person believes, they are no longer under the Law, so as Israel comes to faith, they are no longer held to the penalties of the Law.
Therefore, at that time the Lord will fulfill His covenant to Abraham as promised in Leviticus 26 by releasing the Jewish nations from the penalties of the Old Covenant and giving Israel the Kingdom. In that way, the Abrahamic Covenant makes possible the fulfillment of the Old Covenant (i.e., by placing faith in Jesus).
Until that time, the Old Covenant serves as a guardian of the Jewish people, keeping them under the consequences for their disobedience to the Law. However, no matter how disobedient Israel may be, the Lord will not destroy Israel nor forsake them because of His promises to Abraham. As Paul says:
Gal. 3:17 What I am saying is this: the Law, which came four hundred and thirty years later, does not invalidate a covenant previously ratified by God, so as to nullify the promise.
Gal. 3:18 For if the inheritance is based on law, it is no longer based on a promise; but God has granted it to Abraham by means of a promise.
Gal. 3:19 Why the Law then? It was added because of transgressions, having been ordained through angels by the agency of a mediator, until the seed would come to whom the promise had been made.
The Law serves a purpose of holding Israel under authority until Christ is revealed to the nation. On the day Christ is revealed, the nation will believe and be released from the penalties of the Law, and Paul says the nation's conversion will become riches for all nations, since it leads to the start of the Kingdom: