Pass bill in weird circumstances (7)

I believe the answer is:

outrace

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'pass' is the definition.
Both the definition and answer are verbs in their base form.
Maybe there's a link between them I don't understand?

'bill in weird circumstances' is the wordplay.
I cannot quite see how this works, but
'bill' could be 'ac' (short for account) and 'ac' is found in the answer.
'weird' could be 'outre' (synonyms) and 'outre' is present in the remaining letters.
This accounts for all the letters.
This may be the basis of the clue (or it may be nonsense).

Can you help me to learn more?

I've seen this clue in The Telegraph.

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