Type of headgear (6)
(Other definitions for fedora that I've seen before include "top fashion" , "Felt hat dented lengthways" , "Hat for RAF doe" , "O, Fred, a hat becomes you" , "Felt hat much loved by 1930s gangsters" .)
'type of headgear' is the definition.
This is all the clue.
(Other definitions for fez that I've seen before include "Red hat with black tassel worn by some Muslims" , "High flat-topped red cap with tassel worn by some Muslims" , "Egyptian tasseled hat" , "Brimless conical cap" , "Turkish tasselled cap" .)