The pompous chewed tarragon (8)
I believe the answer is:
arrogant
'the pompous' is the definition.
(thesaurus)
'chewed tarragon' is the wordplay.
'chewed' indicates an anagram.
'tarragon' with letters rearranged gives 'ARROGANT'.
(Other definitions for arrogant that I've seen before include "Self-important and overbearing" , "Cut a design on metal" , "Overbearing; conceited" , "Overly self-important" , "Overbearingly proud" .)