Anger derived from hate (4)
I believe the answer is:
heat
'anger' is the definition.
(thesaurus)
'derived from hate' is the wordplay.
'derived from' is an anagram indicator.
'hate' is an anagram of 'HEAT'.
(Other definitions for heat that I've seen before include "Hotness" , "Vehemence" , "Warm up" , "It's measured in therms" , "early round" .)