Island trying to dispose of seagull droppings? No no (7)
I believe the answer is:
antigua
'island' is the definition.
(I've seen this before)
'of seagull droppings? no no' is the wordplay.
'of seagull' becomes 'anti' (I am not sure about this - if you are sure you should believe this answer much more).
'droppings?' becomes 'guano' (I've seen this before).
'no' is a deletion indicator.
'guano' with 'no' removed is 'gua'.
'anti'+'gua'='ANTIGUA'
'trying to dispose' is the link.
This may not be correct. Some or all of it may belong to another bit of the clue.
Can you help me to learn more?
(Other definitions for antigua that I've seen before include "West Indies island" , "Caribbean island linked with Barbuda" , "One of the Leeward Islands" , "holiday destination" , "Aga unit in the West Indies" .)