Dim female given notice on fourth of June (4)
I believe the answer is:
fade
'dim' is the definition.
(I've seen this before)
'female given notice on fourth of june' is the wordplay.
'female' becomes 'f' (common abbreviation).
'given' is a charade indicator (letters next to each other).
'notice' becomes 'ad' (both can mean an advertisement).
'on' means one lot of letters go next to another.
'fourth of june' becomes 'e' (4th letter of 'june').
'f'+'ad'+'e'='FADE'
(Other definitions for fade that I've seen before include "Waste away" , "Die away" , "Grow dull" , "Gradually disappear from view" , "Lose brightness" .)