The most common and most likely answer to this crossword clue is the 13 letter word VIDEOCASSETTE
I've seen this crossword clue in The Times
V
I
D
E
O
C
A
S
S
E
T
T
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Buddy explains!
The straight part
We know that "Has one got a recording?" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case has one got a recording? = videocassette.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 VIDEOCASSETTE mean?
VIDEOCASSETTE noun- A cassette containing blank or recorded videotape; either in VHS or Betamax format.