Back firm briefly employing family member (6,6)
I believe the answer is:
'family member' is the definition.
(I know that second cousin is a type of relation)
'back firm briefly employing' is the wordplay.
'back' becomes 'second' (both can mean to support an idea or proposal).
'firm' becomes 'co' (a firm is a company).
'briefly' means to remove the last letter.
'employing' becomes 'using' (to employ is to use).
'using' with its last letter taken away is 'usin'.
(Other definitions for second cousin that I've seen before include "Fairly distant relation" , "Some family" , "Relative" .)