These are among the exercises that you can do:
Ask the horse to go in serpentines.  Stiff horses often go through serpentines stiff as a board, their body is straight or they’re even shooting out the shoulder against the movement (as you ask them to go to left, the horse might be shooting out the shoulder to the left).  Training the horse to be able to do good serpentines, with the body bending softly as the horse does the turn (bending in the neck, withers, croup, like a soft u), bending in the poll, is a very good exercise to do at walk, tolt and/or trot, depending on the horse.
Ask the horse to go in circles in the same way, even round circles in different sizes, both left and right circles.
Teach the horse to back, first on the ground, then in the saddle.  Teach the horse to back bent in the poll, and to back mostly by leg-clues (not just from the reins).  The horse is very collected at a backing well performed, and in many cases it works well to ask the horse to back, then walk collected 2-3 steps and then go straight into slow tolt.
Teach the horse leg-yielding, both to the left and to the right.  These exercises help the horse to get suppler, and teaches the horse to listen to clues from each leg.  The same applies to turning on the forehand.
Teach the horse shoulder in and shoulder out at the walk, and then ask the horse to do the same at the tolt, as you get the hang of doing this you will find that most pacy horses go into clean beat when asked to do shoulder in and out at the tolt.  Remember that this is difficult for the horse to do, and only ask the horse to do this for a short time each time.  Shoulder in both helps the horse be more athletic, and it helps collecting the horse.
Gradually these exercises help the horse to clean the beat of the tolt, and to be more athletic.  But this is often a long-term project, both to teach the horse to perform these exercises well, and for the effect to come through on the horse.  After a few weeks you should though be getting results.