For reasons that are unknown to us, God chose Abraham for blessing and called out to him while he was living in Ur of Chaldeans. It may have been because Abraham lived more righteously than those around him. He may have been chosen because God knew that he would respond positively in faith. Or there may any number of other reasons that we simply don’t know.
In this dispensation God begins to work with a group that doesn’t encompass all of humanity. While Noah was singled out, the covenant to him did not begin until he represented all of humanity. Now God has chosen to work specifically with Abraham and his descendents to the exclusion of other people.
The Abrahamic Covenant is first given in Genesis 12:1-4 but is confirmed multiple times to Abraham and his descendents. As it is confirmed, it is fleshed out more. There are three major promises made in the Abrahamic Covenant. The first is that Abraham would be made into a great nation. This promise is made all the more significant when we remember that Abraham’s wife Sarah was barren.
The second promise is actually a series of promises made personally to Abraham. He would be the father of numerous descendants. (This is different from a great nation as Abraham was the father of Ishmael and grandfather to Esau, both of whom grew into nations as well but not the great nation which God would specifically bless.) Abraham would also have his name be made great, be blessed by God, and be a blessing to other people.
The third promise of the Abrahamic Covenant is to the Gentiles. While the dispensation applies to Abraham and his descendants, part of the covenant that God makes with Abraham applies to all other nations. Those who bless Abraham and will be blessed and those who curse him would be cursed. Even more important is that all nations on earth would be blessed through Abraham.
The Palestinian Covenant is given after the giving of the law. It is found in Deuteronomy 28-30, being summarized in 30:1-9. While it takes place in the dispensation of law, it is not really a new covenant so much as another confirmation and expansion of the promise of land given to Abraham. This reinforces the idea that new dispensations do not do away with what God has shown man in the past, it simply adds to it.
The Palestinian Covenant promises dispersion for disobedience, that Israel would repent while in dispersions, that the land would be restored to them, that God would circumcise their hearts, that Israel’s enemies would be judged, and that the nation would return to national prosperity. While Israel was promised the land of Canaan and this covenant promises their return after disobedience, at no point has Israel ever possessed all of the land that God promised them in Number 34:1-12. This promise it still in the future.
The dispensation of promise ended in failure because of a lack of faith. There were no requirements for the Israelites other than to trust God and they couldn’t even do this. Abraham responded in faith when God told him to leave the land of Ur. He responded in great faith when he offered his son Isaac as a sacrifice before God stopped him. The people became a great nation by virtue of the fact that God had promised Abraham this. But they took it for granted. They did not wish to follow Moses when it was time to leave Egypt and did not support him when he confronted Pharoah. They grumbled against God when they wandered in the wilderness, not trusting that God had led them there for a purpose. And they failed to believe that God had given them the land of Canaan and cowered in fear at the report that the land was full of giants. Even after that generation had died off, the Israelites still did not take all of the land that God had promised them and began to make compromises with the idolatrous inhabitants of Canaan.