Country's flag raised with backing of American head of state (7)
I believe the answer is:
eritrea
'country's' is the definition.
(I've seen this before)
'flag raised with backing of american head of state' is the wordplay.
'flag' becomes 'tire' (I've seen this in other clues).
'raised' says the letters should be written backwards.
'with' means one lot of letters go next to another.
'backing of american head of state' becomes 'rea' (I am not sure about this - if you are sure you should believe this answer much more).
'tire' reversed gives 'erit'.
'erit'+'rea'='ERITREA'
Can you help me to learn more?
(Other definitions for eritrea that I've seen before include "It achieved independence from Ethiopia in 1993" , "Country in the Horn of Africa" , "Asmara area" , "State north of Ethiopia" , "River forming part of German-Polish border" .)