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 wordplay.
'factory' becomes 'mill' ('mill' can be a synonym of 'factory').
'outskirts of' says to hollow out the word (remove centre letters).
'exeter' with its middle taken out is 'er'.
(Other definitions for milliner that I've seen before include "Hat-maker", "A maker of women's hats", "Garment maker", "Hat maker", "Philip Treacy, say", "Hatter", "Ladies' hatter", "Felt cutter perhaps", "trader" and "One making pork-pies".)