Left, incensed by the organisation (3,5)
I believe the answer is:
red cross
'the organisation' is the definition.
(Red Cross is an example)
'left incensed' is the wordplay.
'left' becomes 'red' (red can informally mean communist).
'incensed' becomes 'cross' (I am not sure about this - if you are sure you should believe this answer much more).
'red'+'cross'='RED-CROSS'
'by' is the link.
Can you help me to learn more?
(Other definitions for red cross that I've seen before include "seen flying across the country on April twentythird" , "Medical group" , "Famous emblem" , "International organisation to help wounded in war" , "International oranisation for treatment of wounded in war" .)