God promises that he will never again cut off all flesh by the waters of a flood and that a flood will not again destroy the earth Genesis 9:11. The rainbow is given as the sign of this covenant between God and all living creatures Genesis 9:12–17.
In Genesis 9:8–11, God speaks directly to Noah and his sons and announces that he is setting up a covenant. The covenant is not limited to Noah’s family; it extends to Noah’s descendants and to all living creatures that came out of the ark. These verses come just after the flood narrative and after God’s initial instructions to Noah about life in the renewed world (including food and the seriousness of bloodshed). The story now turns from human responsibility to God’s own stated commitment.
Genesis 9:8–11 presents God as the speaker and initiator. He publicly addresses Noah and Noah’s sons, and he announces that he is establishing a covenant.
A careful answer keeps the immediate passage, the book's argument, and the whole-Bible storyline together, so the question is answered in context instead of as a detached idea.
Start with Genesis 9:11, then read the surrounding section so the answer stays connected to the passage's flow.
11I will establish my covenant with you; neither will all flesh be cut off any more by the waters of the flood; neither will there any more be a flood to destroy the earth."