Assuming that pursuers do not encounter any fresh enemy, they move the distance indicated by their dice roll and thereafter are ready to fight normally. So, in their following turn they may charge, march or move normally exactly like any other unit, and no penalty is imposed because of their pursuit move.
It sometimes happens that pursuers move so far that they hit a fresh enemy unit. The pursuers are carried forward against the enemy unit as they chase their fleeing enemy. This is treated as if it were a new charge. However, this will only happen if your direct pursuit move would take you into contact with the enemy. The pursuing unit has no choice in the matter, they must charge against the fresh enemy. The unexpectedly attacked unit can only respond to the charge by holding; any attempt to flee, stand & shoot, or do anything else amidst the confusion of running bodies is deemed impossible. They must make any necessary Psychology tests immediately.
If the new enemy causes fear or terror (see the Psychology section), the pursuers do not have to make a test - they are gripped by the excitement of the chase and are ready to fight any enemy! Note that psychology will apply as normal in the subsequent turns - only the tests required to charge opponents who cause fear or terror are ignored.
Since pursuit into fresh enemy is treated as a new charge, all rules governing charges apply. Specifically, the pursuers must endeavour to bring as many charging models into combat as possible. This means that it will often be necessary to wheel slightly in order to face the enemy.
The resulting combat is worked out in the following turn. The pursuers are charging and so get all the usual benefits and bonuses as if they had charged that turn, even though their charge occurred during the close combat phase of the previous turn. A fleeing unit is destroyed even if its pursuers subsequently charge a new enemy, as long as the pursuing unit's Pursuit roll scores equal to or greater than the fleeing unit's Flee roll.