After first of month, one's going to factory (4)
I believe the answer is:
mill
'factory' is the definition.
(mill is a type of factory)
'after first of month one's going to' is the wordplay.
'after' means one lot of letters go next to another.
'first of month' becomes 'm' (ist letter of 'month').
'one' becomes 'i' (Roman numeral).
'going to' becomes 'll' (as in he'll, we'll etc).
'm' put next to 'i' is 'mi'.
'mi'+'ll'='MILL'
(Other definitions for mill that I've seen before include "Machinery for grinding corn" , "J.S. - - , philosopher" , "(Pepper) grinder" , "English philosopher and economist, d. 1873" , "Grind (flour)" .)