Person imprisoned by king, hopeless case (5)
I believe the answer is:
goner
'hopeless case' is the definition.
(I've seen this before)
'person imprisoned by king' is the wordplay.
'person' becomes 'one' (I've seen this in other clues).
'imprisoned by' means one lot of letters goes inside another.
'king' becomes 'GR' (short for Georgius Rex, King George in Latin).
'one' going into 'gr' is 'GONER'.
(Other definitions for goner that I've seen before include "Hopeless case" , "Something beyond any chance of recovery" , "person about to depart" , "Person beyond saving" , "Someone as good as dead" .)