The most common and most likely answer to this crossword clue is the 6 letter word INDITE
I
N
D
I
T
E
More clues leading to the result INDITE
Buddy explains!

The straight part
We know that "Compose music" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case compose music = indite.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 INDITE mean?
INDITE verb- To physically make letters and words on a writing surface; to inscribe.
- To write, especially a literary or artistic work; to compose.
- To dictate; to prompt.
- To invite or ask.
- To indict; to accuse; to censure.
- An extremely rare indium-iron sulfide mineral.