The most common and most likely answer to this crossword clue is the 16 letter word HUNDRED-YEAR-OLD
I've seen this crossword clue in The Guardian
H
U
N
D
R
E
D
-
Y
E
A
R
-
O
L
D
Buddy explains!
The straight part
We know that "Like the Duke of Edinburgh, soon" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case like the duke of edinburgh, soon = hundred-year-old.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.