If I have The Queen – Wicked and Vain in play and an effect makes me exert her, do I get to draw a card with her I Summon Thee ability?
No. When an ability has a cost, the card’s player must pay that cost to use the ability. If another effect exerts The Queen, you haven’t paid the cost for I Summon Thee, so you don’t get to draw the card. Additionally, you won’t be able to use I Summon Thee until The Queen is readied.
Official set release notes — Fabled