Hardy character taking American student is not appreciated (9)
I believe the answer is:
thankless
'is not appreciated' is the definition.
'hardy character taking american student' is the wordplay.
'hardy character' becomes 'tess' (in Tess of the d'Urbervilles, Thomas Hardy novel).
'taking' is an insertion indicator.
'american' becomes 'hank' (I can't explain this - if you can you should believe this answer much more).
'student' becomes 'l' (as in L-plates for learner drivers).
'hank'+'l'='hankl'
'tess' going around 'hankl' is 'THANKLESS'.
Can you help me to learn more?
(Other definitions for thankless that I've seen before include "Unappreciated" , "Receiving no appreciation" , "Showing no gratitude" .)