Brisk movement of small singer backing Australia (7)
I believe the answer is:
scherzo
'brisk movement' is the definition.
(I've seen this before)
'small singer backing australia' is the wordplay.
'small' becomes 's' (abbreviation - e.g. clothes size).
'singer' becomes 'cher' (American singer).
'backing' shows that the letters should be reversed in order.
'australia' becomes 'oz' (informal name for Australia).
'oz' in reverse letter order is 'zo'.
's'+'cher'+'zo'='SCHERZO'
'of' acts as a link.
(Other definitions for scherzo that I've seen before include "Lively piece of music" , "One often with trio" , "Lively passage" , "Playful musical movement" , "Light or playful movement" .)