Your horse is consistently doing the behavior you want in your shaping session, but how do we get it on cue? Well, it already is on cue - the cue is your shaping session set up. So if you're using a specific body position, target set up, or antecedent arrangement, that is the current cue. So what you really want is to transfer to cue to the new, desired cue.
This is as simple as 'new cue - old cue - bridge/reinforce'.
But to spell it out, you use your desired cue then the cue the horse knows (the set up) then bridge and reinforce. Repeat this in clean loops but each time add more space between the new cue and the old cue, letting the horse predict what you want and respond to the new cue without the old cue. If they don't get it you can remind them and keep connecting the dots. But if they get it keep practicing. Keep practicing in new places, at odd times, with various distractions and mix it in with other behaviors.
Let's use "head down" as an example. We repeatedly lower our target and the horse lowers their head to reach it. Great, we have the behavior on cue, lowering the target. But we want it on verbal cue. So i will say "head down" then lower the target, horse does what i want, bridge/reinforce. I'll repeat this until the horse hears the verbal cue and anticipates, lowering their head without the target. If we got it but the horse looses it, i can give them a hint by gesturing without the target, kind of reminding them what we were doing. Practice until the horse reliably lowers their head on verbal, then practice it in new places, out of context. Make sure we reinforce heavily when the horse responds well around distractions or in difficult situations where things are really different. You can even try mixing it in with different behaviors to test that they know the cue well.