The most common and most likely answer to this crossword clue is the 4 letter word PERE
P
E
R
E
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 = pere.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 PERE mean?
PERE noun- A priest of the Roman Catholic Church, especially a French one. Also used as a title preceding the name of such a priest.
- Sr. - Used after a proper name that is common to a father and his son to indicate that the father is being referred to rather than the son (junior, fils).