Cart shortly setting off, a battle to accelerate (4-6)

I believe the answer is:

drag-racing

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'a battle to accelerate' is the definition.
I can't judge whether this defines the answer.

'cart shortly setting off' is the wordplay.
'cart' becomes 'drag' (synonyms).
'shortly' means to remove the last letter.
'setting off' becomes 'gracing' (I am not sure about this - if you are sure you should give a lot more credence to this answer).
'drag' with its final letter taken off is 'dra'.
'dra'+'gracing'='DRAG-RACING'

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I've seen this clue in The Independent.

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