The most common and most likely answer to this crossword clue is the 6 plus 3 plus 6 letter word EDWARD THE EIGHTH
I've seen this crossword clue in The Daily Telegraph
E
D
W
A
R
D
T
H
E
E
I
G
H
T
H
Buddy explains!
The straight part
We know that "Old monarch" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case old monarch = edward the eighth.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.