Apparently, the live-action adaptation of The Last of Us on HBO isn't playing catch-up to House of the Dragon. Instead, it's the other way around.

Nielsen confirms that HBO's The Last of Us saw a total of 837 million minutes viewed from January 22 through 27, which is more than the 741 million minutes of watch time House of the Dragon had last year.
Considering that the viewing figures for The Last of Us have grown every week since its first episode premiered, it wouldn't surprise us if the TV adaptation ends up usurping the top spot from the likes of Ginny & Georgia, which enjoyed a huge 1.804 billion minutes of watch time across both seasons.
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Arguably, the only bad thing that's happened to HBO's The Last of Us is its four-week streak coming to an end but it's not like it was its own fault. HBO was wise to avoid airing Episode 5 at the same time as Super Bowl LVII last Sunday night and the week-to-week jump was always bound to end.
Because The Last of Us' fifth episode premiered on Friday instead of its usual slot on Sunday, more than half of the people who tuned in to Episode 4 couldn't make it. But, if it's any consolation, Episodes 6 through 9 will be out as intended.
Speaking of The Last of Us, the show's source material, The Last of Us video game series, is expected to get a third game for the PlayStation 6 sometime later this decade.