The full quartet will be back in house (5)
I believe the answer is:
villa
'house' is the definition.
(villa is a kind of house)
'the full quartet will be back in' is the wordplay.
'the full quartet' becomes 'vila' (I can't justify this - if you can you should believe this answer much more).
'be back' indicates one should take the final letters.
'in' indicates putting letters inside.
The final letter of 'will' is 'l'.
'vila' placed around 'l' is 'VILLA'.
Can you help me to learn more?
(Other definitions for villa that I've seen before include "See 3" , "Large country house" , "where 6 [VERDI] lived?" , "Rented holiday home" , "Holiday residence" .)