НЕ ДРЕМАТЬVPsubj: human, collect, or animalusu. past or pres) to be vigilant, watchful, ready to act
X не дремлет - X is wide-awake
X keeps his eyes openX is not asleepX is on the alert
the lookout, his guard )
X is not to be caught napping.
В то время, когда Ираида беспечно торжествовала победу, неустрашимый штаб-офицер не дремал и, руководясь пословицей: «Выбивай клин клином», научил некоторую авантюристку, Клемантинку де Бурбон, предъявить права свои (Салтыков-Щедрин 1). While Iraidka was unconcernedly celebrating her victory, the intrepid staff-officer was not asleep. Guided by the proverb "One nail drives out another," he found an adventuress, a certain Clementinka de Bourbon, and put her up to presenting a claim (1a).
Прошёл слух, что я выступал у курчатовцев, и стали приходить мне многие приглашения... И в этих учреждениях всё как будто было устроено, разрешено директорами, повешены объявления, напечатаны и розданы пригласительные билеты, - но не тут-то было! Не дремали и там (в КГБ) (Солженицын 2). The news that I had appeared at the Kurchatov Institute got around, and invitations began to arrive in large numbers.... These institutions seemed to have everything arranged-directors had given their permission, notices had been put up, invitation cards were printed and distributed-but it was not to be! They (the KGB) were not to be caught napping (2a).