In fact, you need to do the opposite. You should lengthen the reins, lower the hand, and bring your upper body back, keeping the weight in the heel, and focus ahead thinking about what is beyond the jump whilst keeping the energy up and letting the jump come to you.
Many riders focus too hard on the actual jump, which draws the horse into the bottom of the fence, spoiling the distance to make a nice jump. The backward upper body position gives you core strength and a slowing down feeling to the horse and the lowering of the hand stops the temptation to use the reins. You quite often see riders using the reins in a sawing movement, one rein then the other and this throws the horse off balance and makes him want to pull even more. You also need to resist over-folding the upper body over the jump because this again causes a loss of balance and encourages the horse to move faster. Keeping a cool head is so important and hard I know, but if you are consistent with this it will get easier and much more enjoyable for both you and the horse. You will find your jumping will become much smoother and it will prevent the horse feeling he needs to take a pull to get to the jump, making your distance to the jump that much easier.
Training: Gridwork & polework
Gridwork and polework is very good for calming the rushing horse and very good for the rider to practice position. It makes the horse think and control itself. One good exercise to help the horse gain control is a line of canter poles between two jumps on an easy distance. This encourages the horse to keep the stride even between jumps and makes them lower their head, lift their back and round over the jump. Another one is to come to a stop on a straight line. A few strides away a few times if he rushes in front or after the jump if he runs away.
Robert Booth is an equine trainer for Rodgebrook Horses. Visit their website at www.rodgebrookhorses.co.uk or telephone 01983 521870.