Produced cheese from the east (4)
I believe the answer is:
made
'produced' is the definition.
('make' can be a synonym of 'produce')
'cheese from the east' is the wordplay.
'cheese' becomes 'edam' (Edam is an example).
'from the east' says the letters should be written in reverse (on a map from right to left).
'edam' back-to-front is 'MADE'.
(Other definitions for made that I've seen before include "brought about" , "Performed" , "Constructed" , "One renovating (painting)" , "Fabricated" .)