The most common and most likely answer to this crossword clue is the 8 plus 6 letter word PERSONAL STEREO
I've seen this crossword clue in Financial Times
P
E
R
S
O
N
A
L
S
T
E
R
E
O
Buddy explains!
The straight part
We know that "Cassette or CD player" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case cassette or cd player = personal stereo.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.