Embarrassment of King George during succession (7)
I believe the answer is:
chagrin
'embarrassment' is the definition.
(chagrin is a kind of embarrassment)
'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' going inside 'chain' is 'CHAGRIN'.
'of' acts as a link.
(Other definitions for chagrin that I've seen before include "Arching with annoyed disappointment" , "Shame at one's failure" , "Humiliation, mortification" , "irritation?" , "Shame at having failed" .)