Americans awfully keen to invade backward state (7)
I believe the answer is:
yankees
'americans' is the definition.
(Yankee can informally mean an American)
'awfully keen to invade backward state' is the wordplay.
'awfully' indicates an anagram.
'to invade' means one lot of letters goes inside another (inserted letters invade the word).
'backward' says the letters should be written backwards.
'state' becomes 'say' (to state something is to say it).
'say' in reverse letter order is 'yas'.
'keen' is an anagram of 'nkee'.
'nkee' placed inside 'yas' is 'YANKEES'.
(Other definitions for yankees that I've seen before include "Union troops" , "rebellious ex- colonists" , "Northern soldiers in the American Civil War" , "NY baseball team" , "Code words on the radio for US" .)