Cancel housing core of kennels in extension (6)
I believe the answer is:
annexe
'extension' is the definition.
('annexe' can be a synonym of 'extension')
'cancel housing core of kennels' is the wordplay.
'cancel' becomes 'axe' (I've seen this before).
'housing' indicates putting letters inside.
'core of' says to take the centre.
The middle of 'kennels' is 'nne'.
'axe' enclosing 'nne' is 'ANNEXE'.
'in' is the link.
(Other definitions for annexe that I've seen before include "outbuilding" , "Conservatory, e.g." , "Wing of the main building" , "Building joined to another" , "Supplementary part" .)