A number of late nights (3)
I believe the answer is:
ten
'a number' is the definition.
(ten is a number)
'of late nights' is the wordplay.
'of' says the answer is hidden in the clue.
'TEN' is hidden within 'late nights'.
(Other definitions for ten that I've seen before include "PM's address, Downing St" , "X-WORD" , "Base of decimal system" , "Very young" , "Half a score" .)