How do the covenants God made with Israel relate to the Abrahamic covenant?

Every covenant God made with Israel is surrounded by and falls within the bounds of the Abrahamic covenant. The Davidic covenant, for example, is contained within that overarching Abrahamic covenant, showing that all such covenants are subordinate to and encompassed by God's original promise to Abraham.

Les explains that all the covenants God made with Israel are surrounded by the Abrahamic covenant, and every one is within its bounds. He points to the Davidic covenant in 2 Samuel 7 as an example. There, God deals with King David and his royal family, promising a line that would go through Solomon and Nathan, continue down through the genealogy, and eventually reach Joseph and Mary, until Christ was born. Even when the line seemed nearly broken, God preserved it. Thus the Davidic covenant and others are all contained within the Abrahamic covenant.

What is the relationship between the Abrahamic covenant and the other covenants God made with Israel?

The Abrahamic covenant is the overarching framework that contains and surrounds every other covenant God made with Israel. The Davidic covenant, for example, operates within its bounds, continuing the promise line through David, Solomon, and ultimately to Christ. It is not separate but included within that Abrahamic promise.