Feeling ill-used, impoverished earl becomes naturally annoyed at first (9)
I believe the answer is:
indignant
'annoyed at first' is the definition.
'indignant' can be an answer for 'annoyed' (I've seen this before). I am not sure about the 'at first' bit.
I don't understand how the rest of the clue works.
Can you help me to learn more?
(Other definitions for indignant that I've seen before include "Affronted by perceived injustice" , "Miffed" , "Somewhat outraged" , "somewhat angry" , "feeling anger" .)