Stretch stretch stretch! 15 meter circles, spiraling, leg yielding, caveletis
Half halts should be done with your seat, not your hands. Think about rotating your pelvis (like a super subtle pretty cowboy stop, without the legs around the horses chest)
If your horse doesn't respond to that, teach it how to halt with your seat with a stronger pelvic rotation and slight lean back with your torso.
Incorporate heaps of straight rein back, (I reinback by having my seat in the halt position and my legs back behind the girth (10-15cm from it) without any rein pressure) this "forces" the horse to lift his back and use his haunches. Whenever you feel your horse super hollow, do a reinback to remind his this is how you want him to feel. And/or every third or so halt, reinback.
Then, when you have a reinback and a seat halt he will be thinking lift and under because if you halt, he knows he may have to reinback, if it's not a nice halt, reinback (never forcefully or aggressively) and then, while you're w/t/c you can ask for a halt, and he will halt, or, you can ask for a halt and then say actually keep going, with your leg and that my friend is a halfhalt.
So you're thinking about halting, horse goes to halt which get his back up and haunches under to prepare for the halt, then you say keep trotting, so he has the power all coiled up and gives you collection.
You can then have a super light contact with your reins (bit or not)
All lateral exercises really. Shoulder in, travers, renvers, half pass. Horse needs to be balanced and relaxed in order to collect correctly so lateral exercises are great preparation.
Half halts work differently with my horse as she's bitless and I'm honestly finding it harder without a bit...
Half halts work wonders for my horse. My trainer also gave me a description to help with the canter, to work on making it feel like you’re riding up a hill. I also like carrot stretches and longer warm ups because my mare sometimes needs to stretch out before she can properly collect.