It's up to you-- do you want it running concurrently with the Drake Hunt, or should it wait until afterwards?
We can run it concurrently in two seperate seasons. I have seen that technique work in Novus Mane, but at the far extreme I am in a game that seems like a hydra. So just two concurrent stories. I am pretty sure no one will be killed or dramatically changed from the drake hunt, so nothing there will be of significant consequence in the following season.
So I project...
Winter: Drake Hunt
Spring: Mission Impossible
Summer: Council meeting and paychecks
Fall: ???