I finished with an advantage (3-2)

I believe the answer is:

one-up

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'i' is the definition.
Both the answer and definition are adjectives.
Perhaps there's a link between them I don't understand?

'finished with an advantage' is the wordplay.
I cannot quite understand how this works, but
'finished' could be 'up' (eg 'time's up' means the time is finished) and 'up' is located in the answer.
'an' could be 'one' and 'one' is found within the answer.
No letters remain.
This explanation may well be incorrect...

Can you help me to learn more?

I've seen this clue in The Times.

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