Outstanding Liverpudlian singer madly into swing (11)
I believe the answer is:
oscillation
'swing' is the definition.
(thesaurus)
'outstanding liverpudlian singer madly into' is the wordplay.
'outstanding' becomes 'os' (accounting abbreviation).
'liverpudlian singer' becomes 'cilla' (Cilla Black, singer from Liverpool).
'madly' indicates anagramming the letters.
'into' anagrammed gives 'tion'.
'os'+'cilla'+'tion'='OSCILLATION'
(Other definitions for oscillation that I've seen before include "Fast swinging" , "Cycle -- 5 down (anag)" , "Rhythmic swinging to and fro" , "Wavering" , "Movement to and fro" .)