Braggart turns out second hat (6)
I believe the answer is:
boater
'hat' is the definition.
(I know that boater is a type of hat)
'braggart turns out second' is the wordplay.
'braggart' becomes 'boaster' (synonyms).
'turns out' suggests deleting specific letters.
'second' becomes 's' (common abbreviation).
'boaster' with 's' taken away is 'BOATER'.
(Other definitions for boater that I've seen before include "Flat-topped straw hat" , "Hat style" , "sailor, perhaps" , "Stiff hat made of straw" , "Sailor's straw hat" .)