The most common and most likely answer to this crossword clue is the 7 letter word JANACEK
I've seen this crossword clue in Independent
J
A
N
A
C
E
K
More clues leading to the result JANACEK
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 = janacek.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.