Longed to have raced off with victory (6)

I believe the answer is:

craved

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'longed' is the definition.
Although both the answer and definition are past participle verbs, I cannot see how one could define the other.

'raced off with victory' is the wordplay.
'off with' is an anagram indicator.
'victory' becomes 'v'.
'raced' anagrammed with 'v' gives 'CRAVED'.

'to have' acts as a link.

Can you help me to learn more?

(Another definition for craved that I've seen is " 'Desired, longed for (6)'".)

I've seen this clue in The Mirror.

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