Outstanding Liverpudlian singer primarily tackling early swing (9)
I believe the answer is:
oscillate
'swing' is the definition.
(I've seen this before)
'outstanding liverpudlian singer primarily tackling early' is the wordplay.
'outstanding' becomes 'os' (accounting abbreviation).
'liverpudlian singer' becomes 'cilla' (Cilla Black, singer from Liverpool).
'primarily' suggests taking the first letters.
The first letters of 'tackling early' is 'te'.
'os'+'cilla'+'te'='OSCILLATE'
(Other definitions for oscillate that I've seen before include "change sides" , "Swing like a pendulum" , "Swing back and forth" , "Waver between various options" , "Swing to and fro with lost Alice" .)