A house in the southeast part of Mill Hill (4)
I believe the answer is:
semi
'a house' is the definition.
(short for semi-detached)
'southeast part of mill hill' is the wordplay.
I cannot quite understand how this works, but
'southeast' could be 'se' (synonyms) and 'se' is found in the answer.
'part' could be 'mi' (mi is a kind of part) and 'mi' is found in the answer.
This accounts for all the letters.
This may be the basis of the clue (or it may be nonsense).
'in the' acts as a link.
Can you help me to learn more?
(Other definitions for semi that I've seen before include "accommodation" , "Residence" , "home perhaps" , "House attached to one other" , "place" .)