Island's problem with American transport: no terminus (7)
I believe the answer is:
sumatra
'island's' is the definition.
(Sumatra is an example)
'problem with american transport no terminus' is the wordplay.
'problem' becomes 'sum' (as in a mathematical problem).
'with american' becomes 'a' (common abbreviation - e.g. in organisation names. I am not sure about the 'with' bit.).
'transport' becomes 'tram' (method of transport).
'no terminus' means to remove the last letter (terminus means the end of something).
'tram' with its last letter removed is 'tra'.
'sum'+'a'+'tra'='SUMATRA'
Can you help me to learn more?
(Other definitions for sumatra that I've seen before include "Eastern island" , "A US mart on an Indonesian island?" , "Island in western Indonesia" , "Large Indonesian island" , "Large island of Indonesia" .)