Out, local female in hat (9)
I believe the answer is:
published
'out' is the definition.
(I've seen this before)
'local female in hat' is the wordplay.
'local' becomes 'pub' (one's local pub).
'female' becomes 'she' ('she' refers to a woman).
'in' indicates putting letters inside.
'hat' becomes 'lid' (lid can informally mean a hat).
'she' inserted inside 'lid' is 'lished'.
'pub'+'lished'='PUBLISHED'
(Other definitions for published that I've seen before include "Issued" , "Out for all to see" , "available to readers?" .)