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.

Les explains that all these covenants are surrounded by the Abrahamic covenant, and every covenant God made with Israel is within the bounds of that Abrahamic covenant. He points to 2 Samuel chapter 7 as the Davidic covenant. There God deals with David, whose royal family line runs through Solomon and Nathan, the sons of Bathsheba and David, then down through the genealogy to Joseph and Mary and Christ. Les notes the line nearly broke during the Babylonian captivity, which he calls the wasp neck, when only one man in the kingly line could still have a son, but God prevailed and the genealogy continued until Christ was born.

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.