The most common and most likely answer to this crossword clue is the 10 letter word NEANDERTAL
I've seen this crossword clue in The Guardian
N
E
A
N
D
E
R
T
A
L
More clues leading to the result NEANDERTAL
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 = neandertal.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.