Sandor Clegane, aka The Hound, was among the characters considered to kill the Night King at the Battle of Winterfell in Game of Thrones season 8, episode 3, "The Long Night". The HBO show turned the leader of the White Walkers into one of its main villains after his brief introduction in season 4, with the expectation being that everything was building to a final fight between the Night King and Jon Snow, which would bring to an end the clash between the dead and the living.
Game of Thrones certainly teased that showdown on a few occasions, from their face-off during "Hardhome" to another tense stare down during "The Long Night", but showrunners David Benioff and D.B. Weiss had other ideas for who would be granted the honor of killing the show's ostensible Big Bad. Towards the end of the episode's final moments, the shocking sequence finally arrived when Arya Stark killed the Night King, stabbing him with the Valyrian steel catspaw dagger and bringing the Great War to a close.
While that was a triumphant and well-deserved moment for Arya, paying off her years of training in Braavos and even beyond, the Game of Thrones showrunners have previously admitted that they wanted to choose a character that wasn't Jon Snow because him doing it was too obvious. While they ended up with Arya doing the deed, other characters were considered, including the Hound. In James Hibberd's book Fire Cannot Kill A Dragon: Game of Thrones and the Official Untold Story of the Epic Series, the showrunners discuss the decision to have Arya kill the Night King. Hibberd notes that "several hero candidates" were considered, with Benioff saying:
"It had to be somebody with believable access to Valyrian steel. We didn't want it to be Jon because he's always saving the day. We talked about the Hound at one point, but we wanted his big thing to be Clegane Bowl. Ultimately it wouldn't have felt right if it was Jon or Brienne or the Hound.
Game of Thrones had set the Hound up for a big part to play in the battle against the White Walkers, with season 7 connecting him to the Lord of Light as he stared into the flames and had a vision of the mountain he and several other characters would reach in "Beyond the Wall". Although he didn't have a Valyrian steel weapon, it's not implausible he could've got one from someone during the fight (though dragonglass would presumably have worked just as well too). However, given Clegane Bowl was so hyped and the Mountain was the person he most needed to face, it's understandable they wanted to save his big moment for that fight. The Hound did help Arya kill the Night King, not only by assisting her during the battle (after overcoming his own fears), but by being among those who helped train her into the deadly killer she was by season 8, including teaching her where the heart is.
Going back to Benioff's comments, then Brienne of Tarth was seemingly also in the running to kill the Night King, which makes sense since she wielded the Valyrian steel sword Oathkeeper. That might also mean Jaime Lannister was in contention as well, as he had the Valyrian steel sword Widow's Wail in his possession, and was cited as an outside bet of being the one to kill the Night King (giving new meaning to his Kingslayer nickname). The other Valyrian steel weapon in-play at the Battle of Winterfell, besides Jon's Longclaw, was Heartsbane, the ancestral sword of House Tarly, which Sam Tarly gave to Jorah Mormont at the outset of the battle. Sam killing the Night King would've been an interesting (if unlikely) twist, while it's also had to imagine Jorah doing it.
While Arya wasn't a character many thought would kill the Night King in Game of Thrones, it's also hard to argue against her being the right choice in the end, given the payoff it gives to much of her story arc (even if the story with the White Walkers could've been given more room, but that's a much broader issue). As Benioff explains in the book, the dagger in Sam's book at the Citadel confirmed to them that it had to be Arya who killed the Night King, saying "it goes back to the whole 'not today' thing." With the Night King effectively serving as the God of Death, she got her moment, but for the Hound and several other characters, it was a case of "not today" for them doing it.