The Hound's Unfinished Business Is Killing His Brother

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During the episode, we saw The Hound head off to King's Landing where he told Arya he had unfinished business. Earlier in the episode, he told Sansa that there was only one thing that would make him happy. From those two clues, everyone is expecting a Clegane brother showdown (which has been named Cleganebowl).

If you remember, The Hound's brother is the half-man, half-monster that protects Cersei called The Mountain. The Hound has always hated his brother and during their mini-reunion in season seven, he promised to execute him as soon as he had the chance.