So when horse speeds up as someone on the ground to tell you IF horses hind legs are coming to middle of belly. If they are, even though horses is "fast" (tempo) you're headed in the right direction.
If hind legs are not tracking up/ Overtracking (some horses don't have the confirmation to "really" overtrack) take a crop/whip and "pop' him behing your legs. If he runs - let him - idea is to first get forward.
Once you've got the forward the next step is slowing the tempo (and here's the hard part) without loosing the "GO" you just got. It's hard for the horse to push and carry with their butts, hence they would rather fall on their forehand and rush forward.
Easiest pace to slow is the trot. So while keeping your legs on the horse (NOT constant "nagging" with the legs - rather using them the second horse starts to take smaller steps) post slower.
Yes - posting slower than the horse is trotting will tend to throw you off balance. So grab mane, a bucking strap, or anything to keep your balance (if you need it) and start posting at the speed YOU want. Note that some horses naturally have faster trots than others. So when you initially start "slowing" horses trot it may be faster than you want - but give horse time to develop the muscle he/she needs to do more "carry" and then they will be able to slow the trot tempo even more.
Eventually if you are careful NOT to allow horse to "get behind your leg" while getting horse to slow its tempo - you will have a horse with impulsion.
A test I used to do on one mare I own to tell if she was "in front of my leg" - I would ask for a walk/canter transition. If she took even 1 step of trot before she cantered she was behind my leg. I would boot her forward (or a single pop of the whip), slowly bring her back to the walk again (cause boot/whip means she should have leaped forward), then ask again. I normally always got a clean transition after that. It was my "self test" just before I went into the arena.
So idea of that self test is rider asks normally (not a BIG boot/whip smack) and if little or no response then rider asks with a BIG request (BIG boot or hard POP with whip), allow horse to bolt/run/gallop/leap forward - do NOT touch reins for a few strides cause horse is going forward as asked, then bring horse back to pre BIG request before once again asking lightly. Horse learns to listen for "light" requests cause most of them do not like the whip or getting booted with the leg.
(Think of that as shouting versus speaking to the horse. If you shout all the time they learn to tune you out - if you whisper they learn to listen all the time to "hear" what you are saying.)