The most common and most likely answer to this crossword clue is the 13 letter word SEVENTY-EIGHT
I've seen this crossword clue in The Guardian
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Buddy explains!

The straight part
We know that "Old record" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case old record = seventy-eight.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 SEVENTY-EIGHT mean?
SEVENTY-EIGHT noun- A gramophone record designed to be rotated at 78 revolutions per minute; a 78
- The cardinal number immediately following seventy-seven and preceding seventy-nine.