Headgear that’s even better (4,3)
I believe the answer is:
'headgear' is the definition.
(flat cap is a kind of headgear)
'even better' is the wordplay.
'even' becomes 'flat' ('flat' can be similar in meaning to 'even').
'better' becomes 'cap' (I've seen this before**).
'that's' is the link.
(Other definitions for flat cap that I've seen before include "Headgear (of the working class?)" , "working-class symbol" , "Style of headgear" , "> lid" , "Type of hat" .)