The drunken sot possibly sent out for a hat (7)
I believe the answer is:
stetson
'for a hat' is the definition.
(Stetson is an example)
'the drunken sot possibly sent out' is the wordplay.
'the drunken' indicates anagramming the letters.
'possibly' indicates anagramming the letters.
'out' means one lot of letters goes inside another.
'sent' with letters rearranged gives 'sten'.
'sot' anagrammed gives 'tso'.
'tso' going within 'sten' is 'STETSON'.
(Other definitions for stetson that I've seen before include "Hat, for country-and-western singer perhaps" , "Tip" , "A wide-brimmed cowboy hat" , "Large hat" , "Hat, for Texan oil magnate, say" .)