Relief organisation annoyed by communist (3,5)
I believe the answer is:
red cross
'relief organisation' is the definition.
(I've seen this before)
'annoyed by communist' is the wordplay.
'annoyed' becomes 'cross' (cross can mean angry).
'by' says to put letters next to each other.
'communist' becomes 'red' (red can informally mean communist).
'cross' after 'red' is 'RED-CROSS'.
(Other definitions for red cross that I've seen before include "International team" , "Medical group" , "Humanitarian outfit" , "International oranisation for treatment of wounded in war" , "flag" .)