Both sides in dispute right to show anger (6)
I believe the answer is:
dander
'anger' is the definition.
(dander is a kind of anger)
'both sides in dispute right to show' is the wordplay.
'both sides in' says to hollow out the word (remove centre letters) (only the side letters remain).
'right' becomes 'r' (common abbreviation).
'to' is a charade indicator (letters next to each other) (I've seen this in other clues).
'show' becomes 'dan' (I can't explain this - if you can you should believe this answer much more).
'dispute' with its middle removed is 'de'.
'de'+'r'='der'
'der' put after 'dan' is 'DANDER'.
Can you help me to learn more?
(Other definitions for dander that I've seen before include "Hackles" , "One got up by the angry" .)