Who would have the strongest claim to power if Kim Jong Un were to die tomorrow? Does his sister have the strongest claim, or is she likely to get shun by the North Korean elites, because she's a woman? Who would then have the strongest claim to power and why?
Fact is we don't really know, but that can be considered an answer in itself.
To quote Winston Churchill (possibly):
Kremlin political intrigues are comparable to a bulldog fight under a rug. An outsider only hears the growling, and when he sees the bones fly out from beneath it is obvious who won.
The Economist had IIRC an article about a year ago outlining about how some of Kim Yo-jong's new foreign policy assertiveness was probably to bolster her credentials if it came to a succession, despite being a woman.
But you also have to remember that the Kims preside over a system that has nothing to envy in paranoia over the Borgias and Cesars' succession-by-poisoning. Kim had his uncle, who helped secure his power when he first came in as a young whippersnapper, executed, reportedly using AA guns.
The two men, Ri Ryong-ha and Jang Su-gil, were torn apart by antiaircraft machine guns, according to South Korea’s National Intelligence Service. The executioners then incinerated their bodies with flamethrowers.
Jang Song-thaek, widely considered the second-most powerful figure in the North, fainted during the ordeal, according to a new book published in South Korea that offers a rare glimpse into the secretive Pyongyang regime.
“Son-in-Law of a Theocracy,” by Ra Jong-yil, a former deputy director of the National Intelligence Service, is a rich biography of Mr. Jang, the most prominent victim of the purges his young nephew has conducted since assuming power in 2011.
Mr. Jang was convicted of treason in 2013. He was executed at the same place and in the same way as his deputies, the South Korean intelligence agency said.
In other words, as James K said before: we don't really know and we won't know until it happens, that's in the very nature of these systems. Who will horse trade what, backstab whom and what skeletons will be yanked out of closets to rise to the top? There's a small group of successors whose life depend on picking the right side.
Recommended viewing: Death of Stalin, check how Beria lost from being the most likely successor and scaring everyone into alliance against him. Yes, it's a comedy, but the gist was still correct.
A Reuters article from May 1, 2020 examined the issue in a manner that remains sound.
While there is not a clearly established line of succession, the bottom line is that Kim Yo Jong, the current leader's younger sister, or Choe Ryong Hae, who is North Korea's nominal head of state, would be most likely to become the ruler of North Korea if Kim Jong Un died.
Conventional wisdom gives Kim Yo Jong a better shot at winning a power struggle over the succession than Choe Ryong Hae, because Kim Jong Un appears to have been introducing her to roles that prepare her for a top leadership position, and because North Korean politics has tended to favor blood over official leadership position in the past.
Kim Yo Jong, who is Kim Jong Un's "younger sister has been the most visible presence around the leader in the past two years, serving formally as a vice director of the ruling Workers’ Party’s powerful Central Committee but unofficially as her brother’s chief of staff." Some believe that the surviving leadership would not accept a woman in that role, however.
She has received consideration because other relatives of Kim Jong Un seem unlikely to rule. She also seems to be cut from the same ruthless cloth as Kim Jong Un in matters of state.
"Kim Jong Chol is the leader’s older brother but has not been part of the country’s leadership . . . He is believed to be disinterested in public life and is unlikely to emerge as a major presence[.]"
Meanwhile, "Kim Kyong Hui was once a powerful figure in the leadership circle when her brother Kim Jong Il ruled the country. But she has not been seen since her husband, Jang Song Thaek, once regarded as the second most powerful man in the country, was executed in 2013 by Kim Jong Un."
Kim Jong Un's children are just too young to serve in that capacity:
Kim Jong Un is believed to have three children with Ri Sol Ju, the youngest born in 2017, according to the South’s National Intelligence Service. The oldest is a 10-year-old son, meaning any of the three would need the assistance of their relatives or political guardians if they were to become a fourth-generation hereditary leader.
Several party leaders would also be potential successors.
"Choe Ryong Hae is North Korea’s nominal head of state last year as president of the Presidium of the Supreme People’s Assembly." But "Choe and Pak Pong Ju, a fellow politburo member and former state premier . . . are likely to be the figureheads leading a collective leadership," if they took office.
"Kim Yong Chol, a party vice chairman and former top nuclear envoy not related to the Kim dynasty, and Foreign Minister Ri Son Gwon could be tasked with handling diplomatic issues."
To add to the answer by Italian Philosophers 4 Monica, one might ask
- if there is a succession plan right now,
- who that designated successor is, and finally
- if the plan will come through.
Various outside Pyongyang analysts point to the likely importance of the OGD, the Organization and Guidance Department. This report is a bit dated, but it lists a number of power circles. Here and here are articles highlighting the new First Secretary role. I doubt that Westerners with access to classified information know, those of us limited to open sources can only wonder. (And note that professional korea-watchers might have an agenda, if only to get visibility and secure further research funds.)