Does perhaps run after girl (4)
I believe the answer is:
deer
'does perhaps' is the definition.
(I've seen this before)
'run after girl' is the wordplay.
'run' becomes 'r' (cricket abbreviation).
'after' is a charade indicator (letters next to each other).
'girl' becomes 'dee' (name for a girl**).
'r' put after 'dee' is 'DEER'.
(Other definitions for deer that I've seen before include "Antler-bearing animal" , "Antlered animal" , "The - Hunter, 1978 film" , "Grazing animal(s)" , "Perhaps fallow" .)