Country garden designed by American (7)
I believe the answer is:
grenada
'country' is the definition.
(I know that Grenada is a country)
'garden designed by american' is the wordplay.
'designed' is an anagram indicator (designed with the letters).
'by' means one lot of letters go next to another.
'american' becomes 'a' (common abbreviation - e.g. in organisation names).
'garden' is an anagram of 'grenad'.
'grenad'+'a'='GRENADA'
(Other definitions for grenada that I've seen before include "A garden (anag) - Caribbean island" , "Dare nag go to the West Indies?" , "Island state in the West Indies" , "Commonwealth country" , "Island N. of Trinidad" .)