There is NO clear successor after Un. That may be one reason why he’s assinating his family members at an alarming rate!!! The best answer that I’ve found says “Kim Jong Un isn’t the leader of the DPRK. Kim Il Sung is still the leader even in death. Any family member in the lineage is able to take over. Kim Jong Un has many siblings and cousins.”
I also discovered that he has more children tha just the daughter named above; so, one of them might go for it. I assume that much like his father that he will name who HE wants to follows him once he is actualy on his deathbed!!!