Ike is wrong about the soft hat (4)
I believe the answer is:
kepi
'hat' is the definition.
(I've seen this before)
'ike is wrong about the soft' is the wordplay.
'is wrong' indicates anagramming the letters.
'about' is an insertion indicator.
'the soft' becomes 'p' (musical abbreviation for 'piano').
'ike' anagrammed gives 'kei'.
'kei' enclosing 'p' is 'KEPI'.
(Other definitions for kepi that I've seen before include "Military cap with circular top" , "What French soldier may assume" , "Flat-topped military cap" , "Service cap" , "French military cap" .)