The most common and most likely answer to this crossword clue is the 4 letter word MEDE
I've seen this crossword clue in The Daily Telegraph
M
E
D
E
More clues leading to the result MEDE
Buddy explains!

The straight part
We know that "One of the old people" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case one of the old people = mede.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.