Such things can evolve in Dungeon World, but pre-planning big plot points like that doesn't end up working very well. It's awkward, the game will fight it, and the result won't be that much fun for either you or the Cleric's player.
What Dungeon World wants is moments of spotlight. Short moments, consistently and often, are how Dungeon World expects you to give PCs chances to shine. Short moments also makes them lower-pressure for the more quiet players. There are lots of moves you can use for this. (You can even do any of these when another player rolls a miss, allowing you to move the spotlight onto the Cleric as part of your GM move! That is an excellent use of a miss, I find, as it not only helps with spotlight time, but also makes the game feel more dynamic and fluid.):
You could give an opportunity that fits her class:
The ogre bashes Thief into the ground, then stomps off to find Fighter again. Hey Cleric, the ogre isn't paying any attention to you and Thief looks pretty hurt from here, what do you do?
The Mayor is clearly lying, but it's not obvious why she would lie. Hey Cleric, you can read minds with a little bit of work, right? Want to? She's paying attention to the crowd right now, so you can probably pull off a spell without automatically drawing her attention…
Remember, GM moves aren't always bad!
You could separate them so Cleric has some alone time in the spotlight:
You tumble down the sudden and slippery tunnel slope. You land with a bump… alone. Some trick of the stalagmites must have channeled you each down a different branch of the downward tunnel. Cleric, you see [stuff], what do you do?
You can show signs of an approaching threat, but that only Cleric notices (or maybe that only Cleric can notice):
Cleric, while the ogre and Fighter are occupied with each other, you notice a dark cloud moving toward you all, coming over the trees. A moment later and you realise it's a dense swarm of flying insects. It'll probably be here within a minute. What do you do?
There's a presence hanging over the angry mob. You can all feel something, but Cleric, you can suddenly see it. It's a shining — angel, looks like? Huh. What do you do?
You can reveal an unwelcome truth to the Cleric about something she'd be more readily perceptive about than any other PCs, or perhaps just more perceptive about currently:
Cleric, the Mayor's speech is suddenly touching on religious themes, but in a way that gives you a sinking feeling that she's about to renege on the deal and hang you all out to dry. And in front of the King, no less. What do you do?
Any time someone rolls a miss, or the group looks to you to find out what happens, or you're otherwise given a Golden Opportunity, you can pick a move and use it to throw the spotlight on one PC exclusively, to see them shine and learn more about who they are. In this way, you can tweak how much screen time a PC and their player gets. When you have quiet players mixed with outgoing ones, this is an excellent built-in tool Dungeon World puts in your hand to help balance them a little bit.
In my experience, its best to use these with a clear “call to action”. Don't give a timid player an open-ended, ambiguous situation — give them a clear opportunity or danger with an obvious opening to do something. (They can always choose to do something else, anyway.) Having one clear option prevents them from shrinking away from the spotlight as often. I often make moves that are fairly open-ended (I'm working on tightening up my GM moves…), and quiet players don't respond to them as well as focused GM moves.
And beware, too, casually making hard moves that throw the spotlight onto the timid player — the point is to move the spotlight at all and create a welcome gap for the player to insert their contribution into, but making the move too hard can give them paralysis all over again, defeating your effort. It's sufficient to make soft spotlight-moving moves, especially at first.
So when in doubt, make a “spotlight move” softer than you normally would, and with clearer options than you usually feel the need to.
(One exception: when the timid PC's character is physically separate from the other PCs such that they can't defer the decision to them, I find that more open-ended moves do work well. You just have to be ready to wait patiently, without any pressure, when the timid player has to collect their thoughts before taking action.)
With a few more opportunities to contribute during a session, the quiet players both 1) get their PC more naturally entwined in the larger events of the game, and 2) get opportunities to warm up to speaking out and to knowing their character well enough. As time goes on, they will contribute more on their own than before.