A little way from Abergavenny (3)

I believe the answer is:

ave

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'a little way' is the definition.
'ave' can be an answer for 'way' (abbreviation for avenue, a type of 'way'). I'm not certain of the 'a little' bit.

'from abergavenny' is the wordplay.
'from' says the answer is hidden in the clue.
'AVE' is hidden within 'abergavenny'.

Can you help me to learn more?

(Other definitions for ave that I've seen before include "Roman greeting" , "Cockney's own" , "Latin salutation" , "Hail as to Caesar" , "Hail in old Rome" .)

I've seen this clue in the Evening Standard.

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