Problem with a carrier missing out the last island (7)
I believe the answer is:
sumatra
'last island' is the definition.
'sumatra' can be an answer for 'island' (Sumatra is an example). I am not sure about the 'last' bit.
'problem with a carrier missing out the' is the wordplay.
'problem' becomes 'sum' (as in a mathematical problem).
'with a carrier missing' becomes 'ara' (I can't explain this - if you can you should give a lot more credence to this answer).
'out' means one lot of letters goes inside another.
'the' becomes 't' (the is pronounced as a 't' sound in some dialects).
'ara' going around 't' is 'atra'.
'sum'+'atra'='SUMATRA'
Can you help me to learn more?
(Other definitions for sumatra that I've seen before include "part of Indonesia" , "Large Indonesian island" , "Island in western Indonesia" , "Eastern island" , "Large island of Indonesia" .)