Family member misses initial happiness (7)
I believe the answer is:
elation
'happiness' is the definition.
(elation can mean intense happiness)
'family member misses initial' is the wordplay.
'family member' becomes 'relation' (a relation or relative).
'misses initial' means to remove the first letter (I've seen 'missing initial' mean this).
'relation' with its initial letter taken away is 'ELATION'.
(Other definitions for elation that I've seen before include "Toenail (anag) -- delight" , "Transport" , "Feeling of intense delight" , "There's great joy" , "Feeling of joy for it alone" .)