In fairness, only one in empty cafe (7)

I believe the answer is:

justice

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'in fairness' is the definition.
'Justice' can be an answer for 'fairness' (I've seen this before). I am not certain of the 'in' bit.

'only one in empty cafe' is the wordplay.
'only' becomes 'just' (synonyms).
'one in empty cafe' becomes 'ice' (I can't explain this - if you can you should believe this answer much more).
'just'+'ice'='JUSTICE'

Can you help me to learn more?

(Other definitions for justice that I've seen before include "One of man's 22 20 [SEVEN AGES]" , "amends" , "Judge, magistrate" , "right outcome" , "Fair play" .)

I've seen this clue in The Irish Times.

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