Something worn on the head? Even better! (4,3)
I believe the answer is:
flat cap
'something worn on the head?' is the definition.
I can't tell whether this defines the answer.
'even better' is the wordplay.
'even' becomes 'flat' (similar in meaning).
'better' becomes 'cap' (both can mean to beat somebody else's attempt).
'flat'+'cap'='FLAT-CAP'
Can you help me to learn more?
(Other definitions for flat cap that I've seen before include "> lid" , "working-class symbol" , "Style of headgear" , "Headgear (of the working class?)" , "Type of hat" .)