Slender cook with fat 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')
'slender cook with fat' is the wordplay.
'slender' becomes 'small' ('small' can be similar in meaning to 'slender').
'cook with fat' becomes 'fry' ('fry' can be a synonym of 'cook with fat').
'small'+'fry'='SMALL-FRY'
(Other definitions for small fry that I've seen before include "Young ones in school" , "youngsters?" , "Light cooked meal" , "Not the full English breakfast" , "Unimportant things - minnows?" .)