When using Hostile Takeover on a tapped Irelia Fervent, does Irelia get +1 from the ready?

Yes — she gets the +1. Hostile Takeover resolves its instructions in order (take control, then ready), so by the moment the unit is readied, you are already her controller. Irelia's "when you choose or ready me" is read from the perspective of her controller (CR 191.5.a), so the readied-by-you clause is satisfied even though you're taking her from an opponent.

Worth distinguishing from FAQ #236's note that an opponent readying Irelia doesn't trigger her: there the opponent never gains control of her, so the "you" never applies. Here the control change lands first.

Two notes: if she were already ready, nothing would happen (CR 416.1.b/c, a ready unit can't be readied again), and Hostile Takeover also targets her, so you'd typically net +2 Might for the turn (+1 chosen, +1 readied) — the ready trigger is placed on the chain after the spell finishes resolving.