Papers there cleared out to settle disputes (7)
I believe the answer is:
mediate
'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.)" .)