Crossword Genius

Papers there cleared out to settle disputes (7)

Ross

I believe the answer is:

mediate

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'settle disputes' is the definition.
(I've seen this in another clue)

'papers there cleared out' is the wordplay.
'papers' becomes 'media' (I can't justify this - if you can you should give a lot more credence to this answer).
'cleared out' means to remove the middle letters.
'there' with its centre taken out is 'te'.
'media'+'te'='MEDIATE'

'to' is the link.

Can you help me to learn more?

(Other definitions for mediate that I've seen before include "Help resolve a dispute" , "Intercede" , "try to resolve dispute" , "Arbitrate between parties in dispute" , "ie Tamed (anag.)" .)

I've seen this clue in The Sun.
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