This writer is turning out to be getting better (9)

I believe the answer is:

improving

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'be getting better' is the definition.
(I've seen this before)

'this writer is turning out' is the wordplay.
'this writer' becomes 'im' (I've seen this in other clues).
'is turning out' becomes 'proving' (I can't explain this - if you can you should believe this answer much more).
'im'+'proving'='IMPROVING'

'to' is the link.

Can you help me to learn more?

(Other definitions for improving that I've seen before include "Getting better" , "Recovering" , "Making better" .)

I've seen this clue in The Telegraph.

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