The Mosaic Covenant is “the covenant that Moses mediated between God and Israel at Mount Sinai when Israel received the Law (including the Ten Commandments). Also referred to as the ‘old covenant’ (in contrast with the new covenant of Jer 31:31–34; Ezek 36:25–28) …”
By the time this covenant is made with Israel at Mount Sinai, Abraham has passed away and Moses has picked up up the torch to carry on God’s theocracy or covenant program. Moses and the Israelites have been redeemed and delivered out of 400 years of slavery in Egypt (prophesied in Genesis 15:13-14). They are now being delivered and led by Moses and the presence of God to the land promised in the Abrahamic Covenant. This is the first time the people are identified as a nation. As a nation, promised by God (through the Abrahamic Covenant), headed towards the promised land (through the Abrahamic Covenant), they are lacking a law. So, God provides a law and instruction for how the people are to worship Him:
“Then the Lord said to Moses, ‘Write down these words, for in accordance with these words I have made a covenant with you and with Israel.’ So he was there with the Lord forty days and forty nights; he did not eat bread or drink water. And he wrote on the tablets the words of the covenant, the Ten Commandments.” (Exodus 34:27–28, NASB95)
Pentecost puts it this way:
“After redeeming His people, God gave them at Sinai a covenant for their guidance and protection. A redeemed people have an obvious obligation to their Redeemer, but because of their immaturity and the influence of Egyptian culture on them, the redeemed generation had no concept of how to fulfill their obligation. Thus God graciously gave them the Mosaic Covenant, or the Law.”
This covenant is conditional because if the Israelites obey the Law, they will receive blessings. But if they disobey, there will be punishment and sometimes even disaster. This explanation from God to Moses is recorded in Deuteronomy 28-30. This is where the Mosaic Covenant relates back to the Abrahamic Covenant again. The conditional blessings of the Abrahamic Covenant are dependent upon the obedience to the Mosaic Covenant.
 Major Contributors and Editors, “Mosaic Covenant,” ed. John D. Barry et al., The Lexham Bible Dictionary (Bellingham, WA: Lexham Press, 2016).
 J. Dwight Pentecost, Thy Kingdom Come: Tracing God’s Kingdom Program and Covenant Promises Throughout History (Grand Rapids: Kregel Publications, 1995), 85.