Crossword Genius

Keen, very, to get involved in relief programme? (4)

Ross

I believe the answer is:

avid

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'keen' is the definition.
(both can mean enthusiastic)

'very to get involved in relief programme?' is the wordplay.
I cannot really understand how this works, but
'very' could be 'v' (common abbreviation) and 'v' is found in the answer.
'relief' could be 'aid' (I've seen this before) and 'aid' is found in the remaining letters.
This accounts for all the letters.
This may be the basis of the clue (or it may be nonsense).

Can you help me to learn more?

(Other definitions for avid that I've seen before include "Greedy or eagerly desirous" , "Burning" , "Fanatical" , "Keenly enthusiastic" , "Ardent about diva" .)

I've seen this clue in The Independent.
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