Resolve differences: exonerate sole successor in hearing (5,3,3)

I believe the answer is:

clear the air

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'resolve differences' is the definition.
I don't know anything about this answer so I cannot judge whether it can be defined by this definition.

'exonerate sole successor in hearing' is the wordplay.
'exonerate' becomes 'clear' (synonyms).
'sole' becomes 'the' (I am not sure about this - if you are sure you should give a lot more credence to this answer).
'successor' becomes 'heir' (synonyms).
'in hearing' indicates a 'sounds like' (homophone) clue.
'heir' sounds like 'air'.
'clear'+'the'+'air'='CLEAR THE AIR'

Can you help me to learn more?

(Other definitions for clear the air that I've seen before include "Settle misunderstandings" , "get rid of smog" , "Relieve a situation of tension" , "To simplify the condition" , "Use an extractor fan" .)

I've seen this clue in The Times.

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