Excel in open-air celebration!

I believe the answer is:

outdo

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'excel' is the definition.
(I've seen this before)

'open-air celebration' is the wordplay.
'open' becomes 'out' (I've seen this in other clues).
'air celebration' becomes 'do' (I've seen this in other clues. I am not sure about the 'air' bit.).
'out'+'do'='OUTDO'

'in' is the link.

Can you help me to learn more?

(Other definitions for outdo that I've seen before include "Overcome" , "Beat" , "Cap" , "Surpass - overshadow - excel" , "Exceed" .)

I've seen this clue in The Irish Independent.

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