Woman houses old lover in extension (6)
I believe the answer is:
annexe
'extension' is the definition.
('annexe' can be a synonym of 'extension')
'woman houses old lover' is the wordplay.
'woman' becomes 'anne' (I've seen this before**).
'houses' is an insertion indicator.
'old lover' becomes 'ex' (I've seen this in other clues).
'anne' placed around 'ex' is 'ANNEXE'.
'in' acts as a link.
(Other definitions for annexe that I've seen before include "Building attached to a largerone" , "An addition to a document or building" , "Building attached to a larger one" , "extra space" , "Additional room etc for house" .)