Result leaving Conservative annoyed (4)
I believe the answer is:
sore
'annoyed' is the definition.
(thesaurus)
I don't understand the rest of the clue.
Can you help me to learn more?
(Other definitions for sore that I've seen before include "very much" , "source of distress" , "Painful or informally angry" , "Hard" , "Causing or suffering pain" .)