Firm employing all but one family member (6)
I believe the answer is:
cousin
'one family member' is the definition.
(I know that cousin is a type of kin)
'firm employing all but' is the wordplay.
'firm' becomes 'co' (abbreviation for company).
'employing' becomes 'using' (to employ is to use).
'all but' means to remove the last letter ('all but' can mean 'almost' or 'nearly').
'using' with its final letter taken away is 'usin'.
'co'+'usin'='COUSIN'
(Other definitions for cousin that I've seen before include "An aunt's or uncle's child" , "Kinsman, generally (archaic)" , "Aunt's/uncle's child" , "Close relative" , "Relation, could be kissing" .)