If there are no saddle issues or bit issues... my QUICK TIP is :Leg is very important when looking to collect your horse (one has to push towards the contact). I would try doing leg yield exercises and do not let go of the external rein. Not letting go does not mean being strong, but rather supple and be flexible without letting your horse lose the balance. Don´t use too much leg to the extent that you are "hurrying/rushing" either. Be soft with your aids when the horse has lowered his head and always REWARD him to let him know that that is what you wanted. :) .
If he's holding his head high, try raising your hands up. This will feel slightly uncomfortable to him and hopefully lower his head. But when collecting you start with the hind end and work your way to the head!
If he isn't lowering his head when collecting, then his back isn't rounded, and he isn't properly pushing into the bit. You need to push him more forward before collecting, until you have him lifting his back and using his topline, at which point you can ask for collection. Remember for every amour of rein you use, you need to be using at least twice as much leg.
In your horses case it may also just be you need to half halt more before transitioning into collection and while collecting.
Carry your hands low like Peyton said.
Move your hands either up or down. If it is a curb move them vertically up (not up his neck) or if it is a snaffle move them toward your knees to apply the pressure down. Or try draw reins
Not a dental issue or health issue, had him all checked out