Cook supporting little children (5,3)
I believe the answer is:
small fry
'children' is the definition.
(I have seen 'young children' mean 'small fry' so perhaps 'children' could also mean 'small fry')
'cook supporting little' is the wordplay.
'cook' becomes 'fry' (I've seen this before).
'supporting' is a charade indicator (letters next to each other) (in a down clue, some letters go below others).
'little' becomes 'small' ('small' can be a synonym of 'little').
'fry' after 'small' is 'SMALL-FRY'.
(Other definitions for small fry that I've seen before include "Little fish - trivial things" , "Little fish or folk" , "Unimportant people like tiny fish" , "Unimportant people or things" , "Not the full English breakfast" .)