keep sb on their toes

keep somebody on their toes (to keep somebody constantly alert and attentive, usually by doing unexpected things) -- держать кого-л в постоянном напряжении; держать кого-л в страхе; не давать расслабиться; держать в боевой готовности (перен.)

Example: In order to be good at training security guards, you have to keep the trainees on their toes at all times.

keep sb on the jump
also keep sb on tiptoe