Radical annoyed humanitarian organisation (3,5)
I believe the answer is:
red cross
'humanitarian organisation' is the definition.
(I've seen this before)
'radical annoyed' is the wordplay.
'radical' becomes 'red' (I've seen this in other clues).
'annoyed' becomes 'cross' (I've seen this before).
'red'+'cross'='RED-CROSS'
(Other definitions for red cross that I've seen before include "Emergency organisation" , "Medical group" , "International organisation to help wounded in war" , "International organisation for helping war-wounded" , "International movement" .)