Doomed person — one imprisoned by King George (5)
I believe the answer is:
goner
'doomed person' is the definition.
(I've seen this before)
'one imprisoned by king george' is the wordplay.
'imprisoned by' means one lot of letters goes inside another.
'king george' becomes 'gr' (Georgius Rex).
'one' put inside 'gr' is 'GONER'.
(Other definitions for goner that I've seen before include "one with no life left" , "Person beyond help" , "He's unlikely to recover" , "he's bought it" , "toast" .)