An adverb in "-게" plus 바라다, "wish, hope for", with the adverb setting the intensity — 그렇게 that much, 간절하게 desperately. It covers a long-held wish (the long-wished-for reunion), a request (what am I even asking for?), and a formal hope (I sincerely hope it comes about). Note that two lines are a different verb that only looks the same: 따뜻하게 바라 봐 and 그렇게 바라보도록 are 바라보다, "gaze at", not 바라다.