Herb gets arrogant, cooking (8)
I believe the answer is:
tarragon
'herb' is the definition.
(tarragon is a kind of herb)
'arrogant cooking' is the wordplay.
'cooking' indicates anagramming the letters.
'arrogant' with letters rearranged gives 'TARRAGON'.
'gets' acts as a link.
(Other definitions for tarragon that I've seen before include "Herb coming" , "leaves" , "Herb - a torn rag (anag)" , "(Aromatic plant producing) herb" , "Arrogant sort of herb" .)