Daughter is set a test for aversion (8)
I believe the answer is:
distaste
'for aversion' is the definition.
(synonyms)
'daughter is set a test' is the wordplay.
'daughter' becomes 'd' (genealogical abbreviation).
'set' indicates anagramming the letters (instruction to set the letters).
'a'+'test'='atest'
'atest' anagrammed gives 'taste'.
'd'+'is'+'taste'='DISTASTE'
(Other definitions for distaste that I've seen before include "lack of relish?" , "Repugnance" , "Abhorrence" , "Loathing" , "Feeling of dislike or aversion" .)