Hate engendered by extremely divisive experiment (6)
I believe the answer is:
detest
'hate' is the definition.
(to detest is to hate or loathe)
'extremely divisive experiment' is the wordplay.
'extremely' says to hollow out the word (remove centre letters) (only the extremes of the word are used).
'experiment' becomes 'test' (test is a kind of experiment).
'divisive' with its middle taken out is 'de'.
'de'+'test'='DETEST'
'engendered by' is the link.
(Other definitions for detest that I've seen before include "Find repulsive" , "Not like" , "Cordially laothe" , "can't stand" , "Hate a lot" .)