The Post produced up in Williamsburg (4)
I believe the answer is:
'the post' is the definition.
('mail' can be a synonym of 'post')
'up in williamsburg' is the wordplay.
'up' is a reversal indicator (in down clue: letters go upwards).
'in' says the answer is hidden in the clue.
'liam' is hidden within 'williamsburg'.
'liam' back-to-front is 'MAIL'.
'produced' acts as a link.
(Other definitions for mail that I've seen before include "Paper" , "Posted letters" , "Armour of interlinked metal rings" , "American post from Lima" , "Post or body armour" .)