The most common and most likely answer to this crossword clue is the 5 plus 3 plus 6 letter word JAMES THE SECOND
I've seen this crossword clue in The Times
J
A
M
E
S
T
H
E
S
E
C
O
N
D
Buddy explains!
The straight part
We know that "deposed king" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case deposed king = james the second.The cryptic/wordplay part
In cryptic crossword there's often an wordplay/cryptic part as well.This part involves a more complex hint, such as an anagram, homophone, hidden word, etc.
Sadly, We don't have an explanation for this specific crossword clue yet.