The promise was given to Abraham. Through Jacob, it expanded to include the entire Israelite community. Then there is Isaac.
Abraham is a man of action. The man who attacked the army of four kings with only 318 men, and prevailed, also made a point to ensure his son had a suitable bride, one that was not a daughter of the native Canaanites. Of all you could say about Abraham, you could not call him passive. He had all his Egyptian plunder in a row.
Jacob also is an active agent to the point of wresting God himself, an event that branded the name of his descendants for all of eternity.
And then there is Isaac, the limp rag in the middle. When we get to his account, he rarely does anything on his own volition. He rarely even speaks. Rather, it is Rebekah who seems to be the primary mover of the promise in this portion of the story of the patriarchs.
When Laban wants her to stay ten more days, Rebekah decides to leave the next day with Abraham’s servant, ready to begin her own pilgrimage. When she is called to leave, she doesn’t delay. (Gen. 24:55-59)
When Isaac plans to bless Esau, Rebekah, knowing that God had told her “the older will serve the younger,” forms a plan to correct this action so the promise is passed through the correct son. Jacob has the birthright, and so he should receive the blessing of the first-born.
Unlike Abraham, Isaac doesn’t secure wives for his sons, and Esau marries Hittite women. It is Rebekah who prods Isaac into sending Jacob to the land of her father, to first ensure that Esau does not become another Cain, but also to ensure that Jacob does not marry a Canaanite woman. (Gen 27:46)
Isaac abdicates. Rebekah picks up the slack and thereby ensures that the covenant family will continue. Without Rebekah, Isaac would probably have never left his tent.