The most common and most likely answer to this crossword clue is the 12 letter word NONAGENARIAN
I've seen this crossword clue in The Times
N
O
N
A
G
E
N
A
R
I
A
N
Buddy explains!

The straight part
We know that "Old person" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case old person = nonagenarian.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 NONAGENARIAN mean?
NONAGENARIAN noun- One who is between the age of 90 and 99, inclusive. One who is in his or her tenth decade.
- Being between the ages of 90 and 99, inclusive. In one's tenth decade.
- Of or relating to a nonagenarian.