Crossword Genius

Supply - with speed - see a lass run away first (7)

Ross

I believe the answer is:

agilely

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'away first' is the definition.
Both the answer and definition are adverbs. Perhaps there's an association between them I don't understand?

'supply with speed see a lass run' is the wordplay.
I cannot really see how this works, but
'see' could be 'ely' (see is a place with a cathedral - e.g. Ely) and 'ely' is found within the answer.
'a' is present in the answer.
The remaining letters 'gil' 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?

(Another definition for agilely that I've seen is " With quickness and lightness".)

I've seen this clue in The Independent.
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