Crossword Genius

Very old university, Cambridge, has leaders to give personal assurance (5)

Ross

I believe the answer is:

vouch

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'to give personal assurance' is the definition.
I can't judge whether this defines the answer.

'very old university cambridge has leaders' is the wordplay.
'very' becomes 'v' (abbreviation).
'leaders' indicates taking the first letters.
The first letters of 'old university cambridge has' is 'ouch'.
'v'+'ouch'='VOUCH'

Can you help me to learn more?

(Other definitions for vouch that I've seen before include "warrant" , "Be surety (for)" , "Give personal assurance; guarantee" , "Testify" , "Declare support" .)

I've seen this clue in the Sydney Morning Herald.
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