The most common and most likely answer to this crossword clue is the 8 letter word ARCHIVES
I've seen this crossword clue in Financial Times
A
R
C
H
I
V
E
S
More clues leading to the result ARCHIVES
- Records in waste briefly turning up outside busy place
- Skilful composer makes records
- Expert composer making records
- Line written on skin condition for the records
- Records Central Park herbs
- Rash line precedes historical records
- Record collection formed by shrewd American composer
- Leading scorer gets more than one record
- New cashier wraps first piece of vinyl in record store
- Old records of playful American composer
Buddy explains!

The straight part
We know that "record store" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case record store = archives.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 ARCHIVES mean?
ARCHIVES noun- A place for storing earlier, and often historical, material. An archive usually contains documents (letters, records, newspapers, etc.) or other types of media kept for historical interest.
- The material so kept, considered as a whole (compare archives).
- Natural deposits of material, regarded as a record of environmental changes over time.
- To put into an archive.