Female in front of district judge (4)
I believe the answer is:
find
'judge' is the definition.
(finding is a kind of judging)
'female in front of district' is the wordplay.
'female' becomes 'f' (abbreviation).
'front of' suggests taking the first letters (the letter at the front of the word).
The initial letter of 'district' is 'd'.
'f'+'in'+'d'='FIND'
(Other definitions for find that I've seen before include "Locate or discover" , "Track down" , "Discover by chance" , "Come across" , "Encounter, locate" .)