Uncle lost a right in this family (7)
I believe the answer is:
nuclear
'this family' is the definition.
(nuclear family is a kind of family)
'uncle lost a right' is the wordplay.
'lost' indicates an anagram.
'a right' becomes 'ar' (I've seen this in other clues).
'uncle' with letters rearranged gives 'nucle'.
'nucle'+'ar'='NUCLEAR'
'in' is the link.
(Other definitions for nuclear that I've seen before include "Involving part of an atom" , "Using atomic energy" , "Relating to atomic structure" , "Clue ran oddly to atomic" , "Such a bomb" .)