Uncle misused 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 misused a right' is the wordplay.
'misused' indicates anagramming the letters.
'right' becomes 'r' (common abbreviation).
'uncle' is an anagram of 'nucle'.
'nucle'+'a'+'r'='NUCLEAR'
'in' acts as a link.
(Other definitions for nuclear that I've seen before include "Derived from fission or fusion" , "Using atomic energy" , "Sort of energy" , "Such a bomb" , "kind of war" .)