To keep your horse engaged you first need to be sure to have impulsion in every move you ask. Then, your horse has to be on the bit with his back well placed. Do a lot of exercises which require flexibility such as circles, sepentines,... At walk, trot and canter.
Pole work can also help to keep his hindlegs active.
Good luck! :)
Corrot stretches if you stand by the horses back and ask them to stretch there he'd towards there stomach it helps stretch out there back. I have also tired picking up the horse back leg and stretching them out. It seems to help with stiffness