Greek character evidently defending loud friend in French household (7,6)
I believe the answer is:
nuclear family
'household' is the definition.
(nuclear family is a kind of household)
'greek character evidently defending loud friend in french' is the wordplay.
'greek character' becomes 'nu' (letter from the Greek alphabet).
'evidently' becomes 'clearly' (I can't explain this - if you can you should believe this answer much more).
'defending' means one lot of letters goes inside another (inserted letters are defended).
'loud' becomes 'f' (short for forte - 'loud' in music).
'friend in french' becomes 'ami' (I've seen this in another clue).
'f'+'ami'='fami'
'clearly' enclosing 'fami' is 'clearfamily'.
'nu'+'clearfamily'='NUCLEAR FAMILY'
Can you help me to learn more?