How does this covenant with the beasts of the field, the birds of the heavens, and the creeping things of the ground relate to those covenants already mentioned?

The first thing to note is God’s statement of intent: I will. This links back to Hosea 2:14, where God promises: I will allure her.¹ goes as far as to call this prevenient grace, for it is unconditional and actually enables as well as ensures Israel’s response. The change of Israel’s situation and her hope for the future will not primarily be the result of her repentance, for any change on their part will be empowered by God’s gracious intentions for his people. Tied to God’s promise that he will abolish the bow, Israel’s future is entirely bound up in God’s promises.

Hubbard² argues that Hosea couches these promises in covenant language to reassure God’s people, by linking them back to past covenants, particularly those made with Abraham (Hosea 1:10–11) and David (Hosea 3:5). Despite Israel’s desperate attempts to covenant with the foreign nations surrounding them (Hosea 10:4; Hosea 12:1), not to mention their failure to obey the covenant (Exodus 19:1–25; Deuteronomy 29:1–29), God declares his intention to bind himself to them. Thus Hubbard³ writes: “The future needed a new kind of covenant initiated by Yahweh and guaranteed by his sovereignty. Such we find beginning to be described in Hosea 2:18."