Relief organisation embarrassed and annoyed (3,5)
I believe the answer is:
red cross
'relief organisation' is the definition.
(I've seen this before)
'embarrassed and annoyed' is the wordplay.
'embarrassed' becomes 'red' (someone may blush or go red when embarrassed).
'and' is a charade indicator (letters next to each other).
'annoyed' becomes 'cross' (I've seen this before).
'red'+'cross'='RED-CROSS'
(Other definitions for red cross that I've seen before include "International movement" , "International humanitarian organisation" , "that brings relief!" , "International organisation for helping war-wounded" , "seen flying across the country on April twentythird" .)