Following lateral work with a forward pace will encourage engagement of the quarters. An ideal beginner exercise would be to leg yield to the track, or away if suitably on the aids, on reaching your desired spot, I.e. the track, or the quarter line, ask for canter, then ride the canter forward onto a circle to maintain balance. During the circle ride a forwards trot transition and repeat the leg yield again. After a few attempts you should hopefully find instead of slowing and backing off from the leg yield, the horse is thinking forwards and should take longer steps from behind. This exercise can be altered to suit the level you are currently working at, for example instead of leg yield, try shoulder in to medium trot.