Family member's euphoria after run (8)
I believe the answer is:
relation
'family member's' is the definition.
(a relation or relative)
'euphoria after run' is the wordplay.
'euphoria' becomes 'elation' (I've seen this before).
'after' says to put letters next to each other.
'run' becomes 'r' (cricket abbreviation).
'elation' put after 'r' is 'RELATION'.
(Other definitions for relation that I've seen before include "Oriental kind of family connection" , "Relative" , "Telling" , "Auntie?" , "Eg, father" .)