Poor parentage produces ill feeling (3,5)
I believe the answer is:
bad blood
'ill feeling' is the definition.
(I've seen this before)
'poor parentage' is the wordplay.
'poor' becomes 'bad' (similar in meaning).
'parentage' becomes 'blood' (synonyms).
'bad'+'blood'='BAD BLOOD'
'produces' is the link.
(Other definitions for bad blood that I've seen before include "Ill-feeling (between people)" , "Ill feeling, animosity of sanguinary sort" , "Rancour" , "Hatred - ill-feeling" , "Hostility or ill-feeling, from tainted gore" .)