Discover the absence of our island state (8)
I believe the answer is:
missouri
'state' is the definition.
(Missouri is an example)
'discover the absence of our island' is the wordplay.
I cannot really understand how this works, but
'of' could be 'o' and 'o' is found in the answer.
'island' could be 'is' (geographical abbreviation) and 'is' is located in the answer.
This may be the basis of the clue (or it may be nonsense).
(Other definitions for missouri that I've seen before include "American state's" , "So is rum I alter to the state" , "24th American state to join the Union, 1821" , "Biggest tributary of the Mississippi" , "Flower" .)