Despot's extremely tetchy outburst (6)
I believe the answer is:
tyrant
'despot's' is the definition.
(synonyms)
'extremely tetchy outburst' is the wordplay.
'extremely' means to remove the middle letters (only the extremes of the word are used).
'outburst' becomes 'rant' (a rant is an angry outburst).
'tetchy' with its centre removed is 'ty'.
'ty'+'rant'='TYRANT'
(Other definitions for tyrant that I've seen before include "Oppressive and cruel ruler" , "Person dictating" , "taskmaster" , "Despotic ruler" , "big bully" .)