The most common and most likely answer to this crossword clue is the 13 letter word PATERFAMILIAS
I've seen this crossword clue in The Guardian
P
A
T
E
R
F
A
M
I
L
I
A
S
Buddy explains!

The straight part
We know that "old man" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case old man = paterfamilias.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 PATERFAMILIAS mean?
PATERFAMILIAS noun- A man who is the head of a household, family or tribe.