Use 'crack down' in situations where authority is taking action against rules being broken. School administrators will crack down on cheating during exams.
Pro Tip 2/3
Consequence Connotation
'Crack down' suggests there will be consequences for wrongdoing, usually enforced by authority. To prevent accidents, city officials cracked down on jaywalking with fines.
Pro Tip 3/3
Action Intensity
'Crack down' implies a sudden or increased intensity in enforcement rather than a gentle approach. After the riot, the police cracked down on crowd control to restore order.