Possesses objects Henry discarded in Sussex town (8)
I believe the answer is:
hastings
'sussex town' is the definition.
(town in East Sussex)
'possesses objects henry' is the wordplay.
'possesses' becomes 'has' ('have' can be a synonym of 'possess').
'objects henry' becomes 'tings' (I am not sure about this - if you are sure you should believe this answer much more).
'has'+'tings'='HASTINGS'
'discarded in' is the link.
This may not be right. Some or all of it may belong to another bit of the clue.
Can you help me to learn more?
(Other definitions for hastings that I've seen before include "place of battle" , "East Sussex seaside resort" , "Ten Sixty-Six battle" , "His angst (anag.)" , "Town in East Sussex" .)