Languidly making a silky manoeuvre with a Cadillac (15)
I believe the answer is:
lackadaisically
'languidly' is the definition.
(both can mean lazily or lethargically)
'a silky manoeuvre with a cadillac' is the wordplay.
'manoeuvre with' indicates anagramming the letters.
'a'+'silky'='asilky'
'a'+'cadillac'='acadillac'
'asilky' anagrammed with 'acadillac' gives 'LACKADAISICALLY'.
'making' is the link.
(Other definitions for lackadaisically that I've seen before include "Casually" , "Without caring" .)