Lover's last note on union (4)

I believe the answer is:

beau

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'lover's' is the definition.
(beau is a kind of lover)

'last note on union' is the wordplay.
'last note on' becomes 'bea' (I am not sure about this - if you are sure you should believe this answer much more).
'union' becomes 'U' (common abbreviation as in 'Trades Union Congress').
'bea'+'u'='BEAU'

Can you help me to learn more?

(Other definitions for beau that I've seen before include "Dandy - attentive companion" , "Handsome young lover" , "An old boy friend like Brummel?" , "young man" , "Male admirer; dandy" .)

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

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