Sort of cat, one housed in identical quarters (7)
I believe the answer is:
siamese
'sort of cat' is the definition.
'one housed in identical quarters' is the wordplay.
'one' becomes 'i' (roman numeral).
'housed in' means one lot of letters goes inside another.
'identical' becomes 'same' (similar in meaning).
'quarters' becomes 'se' (south and east, two compass quarters).
'i' inserted within 'same' is 'siame'.
'siame'+'se'='SIAMESE'
(Other definitions for siamese that I've seen before include "Pugnacious aquarium species -- shagginess, if I'm thief (anag)" , "cats?" , "Cat - Thai?" , "like a cat" , "Cat with slanting blue eyes and pale fur with darker points" .)