Even better, one's peaked (4,3)
I believe the answer is:
flat cap
'one's peaked' is the definition.
(hat with a peak)
'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'
(Other definitions for flat cap that I've seen before include "Type of hat" , "working-class symbol" , "Headgear (of the working class?)" , "> lid" , "Style of headgear" .)