The most common and most likely answer to this crossword clue is the 8 letter word PLAYLIST
I've seen this crossword clue in The Times
P
L
A
Y
L
I
S
T
More clues leading to the result PLAYLIST
Buddy explains!

The straight part
We know that "Music radio station will allow" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case music radio station will allow = playlist.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 PLAYLIST mean?
PLAYLIST noun- A list of recorded songs scheduled to be played on a radio station.
- A list of tracks to be played in a particular sequence, as from an audio CD.
- A list of songs, prepared for a band or musical artist, to be performed during a concert; a setlist.
- To include (a track) on a playlist.