Schooling exercises?

Counter canter is great for suppling, ride (in trot) a shallow loop along the long side then at the widest part of the loop ask for canter but on the wrong leg (i.e. the leg on the inside of the loop) then maintain counter canter down the rest of the long side. As you build on this exercise, see if you can maintain counter canter around the corner. Eventually you should be able to take the loop away from this exercise and simply ask for canter on the wrong leg and the horse will understand what you are asking. But build this up slowly, start with a large loop and only maintain the counter canter for a short period.

Shoulder in and any other lateral work (leg yield etc) are great for suppling - but ideally you'd want a trainer to show you how to do all of these exercises.

Changing the bend in all gaits is another simple but good exercise - as you are walking down the long side change the bend to the outside, walk straight for a few strides, then change the bend to the inside. This is good on a circle as well or even a square, keep changing the bend but with a bit of straightness in between.

Dont forget to work long and low after you do any of these exercises, they will be taxing for a horse that is stiff so allow him time to stretch and relax into a longer frame after you have done these exercises.

Just keep doing as many schooling exercises as you can that involve changing the bend, as well as the above exercises - so figures of 8, serpentines, half circles etc. And periods of straight lines with stretching in between to ensure you are not over-doing it. But most importantly, ensure you are supervised by a trainer for a while to make sure your horse is capable of all of the exercises and they can also identify any areas where he is particularly weak and work on those specifically.
 
Counter canter is easier to achieve by asking for it in the normal fashion and then riding a shallow loop.

Other supplying exercises I do are plenty of serpentines - 4 and 5 loop ones in walk, 3 and 4 in trot. Start with a 3 and try and fit more loops in each time.

Spirals in and out (leg yielding) are a great tool as is leg yielding on a straight line.

Turn on the forehand/quarters

Figure of eights across the short side
 
Counter canter is easier to achieve by asking for it in the normal fashion and then riding a shallow loop.

Yes wasnt saying my exercise was the easiest way of achieving counter canter (generally changing the rein without changing the leg is the easiest way to go into counter canter) - mine is a particular counter canter exercise my dressage trainer tought me that is brilliant for suppling and also to really get the horse to learn what leg you are asking them to canter on, eventually in preparation for flying changes.

But there should be plenty of exercises now OP to keep you going - lots of good advice!
 
I've been doing lots of 10-15m circles with two of mine - I ask for the bend and then release so there's nothing for them to fight against or lean on.
Also been doing serpentines - if the bend isn't quite there, I go onto a circle and get the horse soft and bending before moving onto the next loop.

Leg yielding on a circle is another good exercise. I hate it, but it works. ;)
 
Ride one metre from the track - sounds easy but it's not... Once you can Acheive this go from this to the 3/4 line leg yielding and vice versa...
 
Depends how stiff the horse is! Correct circles/serpentines etc are VERY good for suppling, both for a youngster and for older horses. Start with larger circles/turns, and progress to smaller ones. Do each new exercise in walk first until your horse is able to do it without too much effort, then go up to trot until they are happy with it in trot, then canter.

Exercises:
20m circles
20m circles with 10m circles at the quarter points in the circle (so if circling between B and E, 10m circle at B, 10m circle at the centre line, then at E, then the other centre line point etc.).
Figures of eight
20m circle, cutting across the circle to change direction
Leg yielding in-out between 10-15-20m circle.
Riding correct squares, pentagons etc.
Serpentines - 3 or 5 loops.
You can also just make your school smaller - so ride in 1/3 of the school (at one end) as if it was the size of the main school, with changes of rein, circles etc.
Turn on the forehand
Leg yielding to the quarter line and back.

To check that your horse is bending correctly (or none of the above will make much difference), try this:
1) Ride a rectangle/square in the school, where the corners are not the school corners, applying sufficient inside leg that your outside rein feels heavier as your horse goes to bend around your leg but is prevented from doing so by your outside rein. At the corners, give with your outside rein, but change nothing else. If you have your horse between your inside leg and outside hand correctly, your horse will bend and turn the corner. You then take up more contact with your outside rein again to keep the horse straight on the 'straight' bit.
2) Now try this on a circle. Again, with enough inside leg you have weight in your hand, but giving enough to make that nice 20m circle. At the four 'quarter' points, give with your outside hand enough to get the right bend for a 10m circle. As the circle finishes, increase the contact and ask the horse to take the lesser bend that is the next quarter of the 20m circle. Repeat. Make s aure you keep your outside leg slightly behind the girth to ensure the quarters don't swing out though!
3) Practice changing direction (and bend) across a circle, changing over inside leg/outside hand half way across.
 
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