Come cycling around side part of America (6)
I believe the answer is:
mexico
'part of america' is the definition.
(I know that Mexico is part of America)
'come cycling around side' is the wordplay.
'cycling' is an anagram indicator.
'around' means one lot of letters goes inside another.
'side' becomes 'XI' (a football team, from Roman numerals for 11).
'come' with letters rearranged gives 'meco'.
'meco' placed around 'xi' is 'MEXICO'.
(Other definitions for mexico that I've seen before include "Country south of USA" , "Land of the Aztecs" , "Aztec, Maya country" , "Country south of US" , "American country -- eco-mix (anag)" .)