Well, what comes siguiente after "The frozen Throne" is the "Burning Crusade". The burning crusade is a Warcraft online game. On the expansion, you'll witness what happens to Illidan after his duel with Arthas (Yes, he's NOT dead) & so many más events (I haven't played it since I don't really play online games but I know most of the events that took place on the Burning Crusade that affected the Warcraft lore & I don't want to spoil anything :D).
After the Burning Crusade, we have the "Wrath of the Lich King" expansion. It's an online game still that really focused on the aftermath of Arthas' merging with the Lich King. There, you'll witness what happens after Arthas awakens ever since he merged with the Lich King.
If tu want to witness them yourself, you'll have to play the Burning Crusade o the Wrath of the Lich King online games.
If tu want to be spoiled without playing the games, why don't tu read what happened yourself?
Check out this site:
link tu can buscar for anything warcraft-related including the events that took place after Arthas' becoming of the Lich King.
Just ask me anything if you're confused o if tu can't find the stuffs you're looking for at the warcraft wiki. I'll straighten them out for you. :)
(BTW, If tu want to get a small glimpse of the what really happens after Arthas' merge with the lich king, watch the trailer for the "Wrath of the Lich King" online game. ;)