Brag noisily of small bet involving golf (7)

I believe the answer is:

swagger

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'brag noisily' is the definition.
'swagger' can be an answer for 'brag' (thesaurus). I am not sure about the 'noisily' bit.

'small bet involving golf' is the wordplay.
'small' becomes 's' (abbreviation - e.g. clothes size).
'bet' becomes 'wager' (synonyms).
'involving' means one lot of letters goes inside another.
'golf' becomes 'g' (phonetic alphabet: alpha, bravo, charlie etc.).
'wager' going around 'g' is 'wagger'.
's'+'wagger'='SWAGGER'

'of' is the link.

Can you help me to learn more?

(Other definitions for swagger that I've seen before include "Lofty proud gait" , "Show off" , "Walk proudly" , "Blustering arrogance" , "Walk self-importantly, strut" .)

I've seen this clue in The Telegraph.

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