If Dorne has shown us anything on Game of Thrones, it's that the ladies who live there are absolutely vicious when it comes to protecting their own. They'll kill anyone, anywhere if it meets their needs (just ask Myrcella). Even so, it was a major shock when out of nowhere one of the Sand Snakes pulled a knife on their uncle, the ruling king of Dorne, Doran. He was stabbed and left to bleed out, which is not only bad manners but leaves a pretty big question hanging: who will rule Dorne after Doran's death?
In the books the series is based on, the heir to the throne is Doran's eldest daughter, Arianne Martell. However, Arianne is not a character on the television series; instead, Doran's youngest son Trystane was upgraded to the position of heir. Trystane is also Myrcella Baratheon-Lannister's fiance – or at least he was until she was killed. The premiere episode of Season 6 shows that Trystane is alive and well (so far), so it stands to reason that he is set to rule Dorne now that his father is dead. However, the Sand Snakes might have something to say about that.
The Sand Snakes followed up their attack on Doran with an attack on Trystane, and while he certainly seemed ready for a fight, he wasn't able to prevent a spear through the face. With Trystane taken out of the line of succession, there isn't anyone left to take over the throne of Dorne – which might be just what the Sand Snakes are after if they want to grab it for themselves.