The most common and most likely answer to this crossword clue is the 16 letter word AIRCRAFT-CARRIER
I've seen this crossword clue in Independent
A
I
R
C
R
A
F
T
-
C
A
R
R
I
E
R
Buddy explains!
The straight part
We know that "Prince of Wales, say" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case prince of wales, say = aircraft-carrier.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.