We might not have an Ilclan at the end of this. The book title could instead be about the focus on trying, it is what Malvina is burning the universe for. Frankly I think this is the more satisfactory outcome. We do know that there will be an Ilkhan on Terra and we do know that his Loremaster will from a Jade Falcon blood house. But we are still a century off from this, and we do not know if this is the first Ilkhan on Terra or a successor.
I would not be too surprised in the Ilkhan of the clans and First Lord of the Star League become one and the same and it becomes some sort of revolving chair. Do not exclude the possibility that the future Ilkhan is a Successor Lord.
Also remember this, an Ilkhan who tries to impose clan society on Terra will have no end of trouble. Its Terra! You can take away everyones surname or national identity because Nicholas Kerensky or clan honour or so on and so forth. Yes that is important elsewhere but Terra is our collective home. People are French, Chinese, American, Brazilian etc etc, they are not clan subjects. Even Amaris didn't mess with the ancient social structures, semi independent feudal settlements and indigenous tribes.
People in France or Germany has been French or German for a very long time. Now they are expected to conform and be single named cast subjects of clan <insert animal name here>. As soon as Malvina or Alaric declares themselves rulers of Terra and start a clan cultural pogrom, EVERYONE will stand up to stop it. I can see this happening. Nicholas Kerensky was a weird man with weird ideas that can be made to work more or less, but it's an assimilatory system completely at loggerheads with the cultural Marinas Trench his legacy would be trying to wade through if a 'traditional' Ilkhanship is to be imposed on Terra.