<p>First of all, there's no evidence that Arnook didn't have any other children. Just because we didn't see a wife or younger children doesn't mean that they weren't there. Besides, the sexist nature of the Northern Water Tribe would mean that even if Yue had survived, she would not have succeeded her father as chief...that role would go to her younger brother or some other male relative (most likely an uncle or a cousin).
</p><p>It is interesting to note that the only Northern chief we saw in between Arnook and Unalaq was a man presumed to be Tonraq and Unalaq's father. We saw a glimpse of him sitting on his throne as he was banishing Tonraq who was at least in his early 20s at the time. This chief appeared to be a middle-aged man, clearly old enough to be Tonraq and Unalaq's father. And bearing in mind that this took place approximately 50 years after the events of ATLA, it is reasonable to assume that this chief was the son of Arnook and younger brother of Yue. He would have been a very young child at the time of the Fire Nation invasion of the Northern Water Tribe, if he was yet born at all.
</p><p>Perhaps the reason we didn't see him during these events is because Arnook wisely sent is wife and (possibly unborn) heir to the throne away to a safer place when he knew the invasion was coming. This would also make Yue Korra's great-aunt. Of course, this is all assuming that Arnook was succeeded by his son, which is speculation, but it's still fun to imagine.
</p>