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.

Also
keep sb on the jump
also keep sb on tiptoe