State failed doctor in Irish country (4,5)
I believe the answer is:
east timor
'country' is the definition.
(I have seen 'Asian country' mean 'east timor' so perhaps 'country' could also mean 'east timor')
'state failed doctor in irish' is the wordplay.
'failed' indicates an anagram.
'doctor' becomes 'mo' (medical officer**).
'in' indicates putting letters inside.
'irish' becomes 'ir' (abbreviation).
'mo' inserted inside 'ir' is 'imor'.
'state' anagrammed gives 'eastt'.
'eastt'+'imor'='EAST TIMOR'
(Other definitions for east timor that I've seen before include "Part of the Malay archipelago - estimator (anag)" , "island nation" , "Ex-Portuguese colony annexed by Indonesia, independent since 2002" , "Southeast Asian country, independent since 2002, capital Dili" .)