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:
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:
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:
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:
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:
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:
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: