Agent is not finished with the people on this island (8)
I believe the answer is:
republic
'this island' is the definition.
Although both the answer and definition are singular nouns, I don't see how one could define the other.
'agent is not finished with the people' is the wordplay.
'agent' becomes 'rep' (short for representative).
'is not finished' means to remove the last letter.
'with' means one lot of letters go next to another.
'the people' becomes 'public' (public is a kind of people**).
'rep' with its last letter taken away is 're'.
're'+'public'='REPUBLIC'
'on' is the link.
Can you help me to learn more?
(Other definitions for republic that I've seen before include "Commonwealth" , "Cuba, say" , "State in which the people hold the power" , "Cure blip (anag.)" , "Country in which supreme power is held by the people" .)