Not stay for the decisive contest (6)

I believe the answer is:

runoff

I'm a little stuck... Click here to teach me more about this clue!

'contest' is the definition.
(thesaurus)

'not stay for the decisive' is the wordplay.
I cannot quite see how this works, but
'not' could be 'no' (negative) and 'no' is located in the answer.
The remaining letters 'ruff' is a valid word which might be clued in a way I don't understand.
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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