State syrup, heading off cough, has worked (6)
I believe the answer is:
cyprus
'state' is the definition.
(Cyprus is an example)
'syrup heading off cough has worked' is the wordplay.
'heading off' says to take the initial letters.
'has worked' is an anagram indicator (letters must be worked into new positions).
The initial letter of 'cough' is 'c'.
'syrup'+'c'='syrupc'
'syrupc' anagrammed gives 'CYPRUS'.
(Other definitions for cyprus that I've seen before include "Divided Mediterranean island" , "Mediterranean island of Aphrodite" , "Mediterranean island country" , "Othello island" , "European island country" .)