Annoying child with black rodent (4)
I believe the answer is:
brat
'annoying child' is the definition.
(I've seen this in another clue)
'with black rodent' is the wordplay.
'with' is a charade indicator (letters next to each other).
'black' becomes 'b' (abbreviation as in pencil classifications).
'rodent' becomes 'rat' (rat is a kind of rodent).
'b' put next to 'rat' is 'BRAT'.
(Other definitions for brat that I've seen before include "Nasty child" , "Little terror" , "Bad child - pack member!" , "Ill-behaved child" , "Spoilt child" .)