Annoyance shown by King George during succession (7)
I believe the answer is:
chagrin
'annoyance' is the definition.
(I've seen this before)
'king george during succession' is the wordplay.
'king george' becomes 'gr' (Georgius Rex).
'during' means one lot of letters goes inside another.
'succession' becomes 'chain' (I've seen this before).
'gr' put within 'chain' is 'CHAGRIN'.
'shown by' acts as a link.
(Other definitions for chagrin that I've seen before include "Acute annoyance or disappointment" , "Humiliation, mortification" , "Embarrassment - rich nag (anag)" , "Frustration at having failed" , "Strong feeling of embarrassment" .)