Disgusted character sitting outside entrance to Ashmolean (9)
I believe the answer is:
nauseated
'disgusted' is the definition.
('nauseate' can be a synonym of 'disgust')
'character sitting outside entrance to ashmolean' is the wordplay.
'character' becomes 'nu' (nu is a kind of character**).
'sitting' becomes 'seated' ('seated' can be a synonym of 'sitting').
'outside' indicates putting letters inside.
'entrance to' suggests taking the first letters.
The initial letter of 'ashmolean' is 'a'.
'nu'+'seated'='nuseated'
'nuseated' placed around 'a' is 'NAUSEATED'.
(Other definitions for nauseated that I've seen before include "Revolted" , "Disgusted" , "Sickened" .)