Dislikes out-of-the-way millinery (5)
I believe the answer is:
hates
'dislikes' is the definition.
(hating is a kind of disliking)
'out-of-the-way millinery' is the wordplay.
'out of' means one lot of letters goes inside another (some letters on the outside of others).
'the way' becomes 'e' (Compass direction - East).
'millinery' becomes 'hats' (I've seen this in another clue).
'e' put within 'hats' is 'HATES'.
(Other definitions for hates that I've seen before include "Dislikes intensely" , "Detests" , "Despises" , "Abhors" , "passionate feelings" .)