My mind went to the idea that Starke wants her partially as a means of getting more of a handle on Mathilde, both in terms of understanding and of influence. Possibly paranoia on my part, I admit.
You were trained as a Grey Wizard, after all. It's not paranoia if they really are out to get you.
There's something about Starke that has me on edge. Like, I can't get a handle on his personality or his ambitions. He's a worshipper of Sigmar, and in canon uses his faith as a tool to unify people, he's the future canon patriarch of the Grey Order, he currently handles interior security, and the only "big" thing that we know he's done was take out a Tzeentchian cult that targeted the Colleges. All the other LM's are crazy people who protected the empire one broken rule after another, but Starke doesn't fit that sterotype at all—he cleaves too closely to the rules, I feel.
And for the life of me I can't think why he wants Eike specifically as an apprentice. Sure, she's talented, but top pick for the internal security guy? Something's a bit odd there.
I was doing some re-reading and came across the section where Mathilde gave up all that Skaven stuff for the Gehenna's hounds favour and found out about the apparition binding.
Did that result in any further actions? I'd like to explore that option if not so we can get something out of that favour from the Golds. Perhaps we can start researching Apparitions to bind?
Not yet, we're hopefully going to start exploring it in the next few turns, waystones permitting, but the thread has been a bit hesitant over tracking down a totally-not-a-demon, binding it in a way that is not dark sorcery guys, no really trust me, and then laundering that knowledge without implicating the Golds.
Thankfully, we can pretend to have gotten the idea from the Spirits the Eonir have bound, as well as from Hag Witch magic, so we're in a good place to begin it as a research project at the moment, and the option to have attempted to bound Drycha appears to have invigorated the apparition faction.