The most common and most likely answer to this crossword clue is the 16 letter word STICK-IN-THE-MUD
I've seen this crossword clue in The Guardian
S
T
I
C
K
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I
N
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T
H
E
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M
U
D
Buddy explains!
The straight part
We know that "Fogey" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case fogey = stick-in-the-mud.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.
What does STICK-IN-THE-MUD mean?
STICK-IN-THE-MUD noun- A person unwilling to participate in activities; a curmudgeon or party pooper.
- More generally, one who is slow, old-fashioned, or unprogressive; an old fogey.