Discover the absence of our island state (8)
I believe the answer is:
missouri
'state' is the definition.
(I know that Missouri is a American state)
'discover the absence of our island' is the wordplay.
I cannot quite understand how this works, but
'of' could be 'o' and 'o' is located in the answer.
'island' could be 'is' (geographical abbreviation) and 'is' is found within the answer.
This explanation may well be incorrect...
(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" .)