Support composer giving out unknown previous compositions (8)

I believe the answer is:

backlist

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

'previous compositions' is the definition.

'support composer giving' is the wordplay.
'support' becomes 'back' (back is a kind of support).
'composer giving' becomes 'list' (I can't justify this - if you can you should believe this answer much more).
'back'+'list'='BACKLIST'

'out unknown' is the link.
I am not very happy about this link. Some or all of it may belong to another bit of the clue.

Can you help me to learn more?

I've seen this clue in The Telegraph.

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