I am using Irelia Legend, and I target my exhausted stellacorn on a battlefield with discipline, when is the window that I get to use Irelia Legend? Is it after the spell resolves or when I chose it for the spell?

You get the window immediately — the moment you choose the Stellacorn as the target of Discipline, not after the spell resolves.

Choosing a target happens during finalization of the spell (Rule 355.5), and that "choose a friendly unit" is the trigger event for Blade Dancer (Rule 383). The Legend ability is placed on the Chain on top of Discipline, so because the Chain resolves last-in-first-out, Blade Dancer resolves before Discipline does. You can't hold the trigger for later — but you don't need to, since readying happens first anyway.

Sequence: play Discipline → choose Stellacorn → Blade Dancer triggers → you exhaust the Legend, pay [A], ready the Stellacorn → then Discipline resolves giving +2 Might and drawing 1. (This is exactly the sequencing in RiftJudge FAQ #703.) If you don't want to use Blade Dancer, you can decline the "you may" during finalization of the trigger.