Unwell after minutes in factory (4)
I believe the answer is:
mill
'factory' is the definition.
('mill' can be a synonym of 'factory')
'unwell after minutes' is the wordplay.
'unwell' becomes 'ill' ('ill' can be similar in meaning to 'unwell').
'after' says to put letters next to each other.
'minutes' becomes 'm'.
'ill' put after 'm' is 'MILL'.
'in' is the link.
(Other definitions for mill that I've seen before include "Place for grinding flour" , "Race a moving influence on this" , "(Pepper) grinder" , "Advocate of the utilitarian" , "Grind to a powder or dust" .)