The kind looked for, say (4)
I believe the answer is:
sort
'the kind' is the definition.
('sort' can be a synonym of 'kind')
'looked for say' is the wordplay.
'looked for' becomes 'sought' ('seek' can be a synonym of 'look for').
'say' shows a homophone (sound like).
'sought' is a homophone of 'SORT'.
(Other definitions for sort that I've seen before include "Classify; kind" , "Arrange; category" , "choice of characters frequently used in statistics" , "'Variety, type (4)'" , "Put in order" .)