The most common and most likely answer to this crossword clue is the 4 letter word KERN
I've seen this crossword clue in The Guardian
K
E
R
N
Buddy explains!

The straight part
We know that "composer/composer" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case composer/composer = kern.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 KERN mean?
KERN noun- A corn; grain; kernel.
- The last handful or sheaf reaped at the harvest.
- The harvest home.
- Any part of a letter which extends into the space used by another letter.
- (chiefly proportional font printing) To adjust the horizontal space between selected pairs of letters (characters or glyphs); to perform such adjustments to a portion of text, according to preset rules.
- A light-armed foot soldier of the ancient militia of Ireland and Scotland; in archaic contexts often used as a term of contempt.
- A boor; a low person.
- An idler; a vagabond.
- A mill for grinding corn, especially a hand-mill made of two circular stones.
- A churn.