Produced edam, possibly (4)
I believe the answer is:
made
'produced' is the definition.
('make' can be a synonym of 'produce')
'edam possibly' is the wordplay.
'possibly' indicates an anagram.
'edam' is an anagram of 'MADE'.
(Other definitions for made that I've seen before include "Manufactured" , "Forced" , "brought about" , "Constructed" , "Performed" .)