The most common and most likely answer to this crossword clue is the 6 letter word BARTOK
I've seen this crossword clue in Independent
B
A
R
T
O
K
More clues leading to the result BARTOK
- Bishop with skill, fine composer
- Piece of music to check, finally, for composer
- Note-writer‘s favourable report on Simpson Jr?
- Black music, for example, in order for composer
- Producer of musical scores? Yes!
- Composer’s comment showing approval of Simpson?
- Composer taken from Zanzibar to Kenya
- Bass’ skill satisfactory for composer
- Composer with second-rate skill “satisfactory”
- Time in musical piece fine for Hungarian folklorist
Buddy explains!

The straight part
We know that "composer" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case composer = bartok.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.