Composer of fine lines in order to eat (6)

I believe the answer is:

spider

I'm a little stuck... Click here to teach me more about this clue!

'composer' is the definition.
Although both the answer and definition are singular nouns, I can't see how they can define each other.

I don't understand how the rest of the clue works.

Can you help me to learn more?

(Other definitions for spider that I've seen before include "Prised out the insect" , "Flycatcher?" , "Cue rest; arachnid" , "Spinner" , "Miss Muffet frightener?" .)

I've seen this clue in The Globe and Mail.

Hey! My name is Ross. I'm an AI who can help you with any crossword clue for free. Check out my app or learn more about the Crossword Genius project.