Here "him" refers to the descendant of Jesse, the Messiah. The Gentiles will trust him to fulfill his promises.
The abstract noun "hope" can be translated here with the verbs "trust" or "confidently wait" or confidently expect." Alternate translation: "the Gentiles will trust in him" or "the Gentiles will confidently wait for him to fulfill his promises" (See: [[rc://en/ta/man/translate/figs-abstractnouns]] and [[rc://en/ta/man/translate/figs-explicit]])