The most common and most likely answer to this crossword clue is the 3 plus 3 letter word OFF AIR
I've seen this crossword clue in Independent
O
F
F
A
I
R
Buddy explains!

The straight part
We know that "not being played on the radio" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case not being played on the radio = off air.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 OFF AIR mean?
OFF AIR adjective- Not broadcast on radio or television.
- Pertaining to a radio or television station that is completely shut down.