The most common and most likely answer to this crossword clue is the 8 plus 6 letter word MAGNETIC STRIPE
I've seen this crossword clue in The Times
M
A
G
N
E
T
I
C
S
T
R
I
P
E
Buddy explains!
The straight part
We know that "Electronic data repository" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case electronic data repository = magnetic stripe.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.