Race to eat a hot dog in America? (6)
I believe the answer is:
hurray
'hot dog in america?' is the definition.
('hot dog' is a US interjection similar to hurray)
'race to eat a' is the wordplay.
'race' becomes 'hurry' (synonyms).
'to eat' means one lot of letters goes inside another.
'hurry' enclosing 'a' is 'HURRAY'.
(Other definitions for hurray that I've seen before include "very brief message of joy" , "Yippee!" , "cheer" .)