Just the day before, postman finally delivered (4-6)

I believe the answer is:

even-handed

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'just' is the definition.
(I've seen this before)

'day before postman finally delivered' is the wordplay.
'day before' becomes 'eve' (the eve of something is the night before).
'finally' suggests the final letters.
'delivered' becomes 'handed' (I can't justify this - if you can you should give a lot more credence to this answer).
The final letter of 'postman' is 'n'.
'eve'+'n'+'handed'='EVEN-HANDED'

'the' is the link.

Can you help me to learn more?

(Another definition for even-handed that I've seen is " Fair, impartial".)

I've seen this clue in The Times.

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