Hat maker's factory in outskirts of Exeter (8)
I believe the answer is:
Here is my best explanation:
'hat maker's' is the definition.
(I've seen this before)
'factory in outskirts of exeter' is the subsidiary indication.
'factory' becomes 'mill' ('mill' can be a synonym of 'factory').
'outskirts of' says to hollow out the word (remove centre letters).
'exeter' with its centre removed is 'er'.
(Other definitions for milliner that I've seen before include "A maker of women's hats", "Hat maker", "Felt cutter perhaps", "Garment maker", "Hatter", "Ladies' hatter", "Hat-maker", "trader", "One making pork-pies" and "Maker of women's hats".)