Delight when family member doesn't start (7)
I believe the answer is:
elation
'delight' is the definition.
(I've seen this in another clue)
'family member doesn't start' is the wordplay.
'family member' becomes 'relation' (a relation or relative).
'doesn't start' means to remove the first letter.
'relation' with its first letter taken off is 'ELATION'.
'when' acts as a link.
(Other definitions for elation that I've seen before include "High feeling?" , "Feeling of delight or pride" , "Euphoria of toenail" , "Bliss" , "State of being delighted or proud" .)