In the hands of a smooth operator from Park Lane on one side of Westminster (6)
I believe the answer is:
planer
'in the hands of a smooth operator from park lane' is the definition.
I can't tell whether this defines the answer.
'on one side of westminster' is the wordplay.
'on' means one lot of letters go next to another.
'one' becomes 'ane' ('ane' can be a synonym of 'one').
'side' becomes 'r' (abbreviation for right).
'of westminster' becomes 'pl' (I am not sure about this - if you are sure you should believe this answer much more).
'ane'+'r'='aner'
'aner' after 'pl' is 'PLANER'.
Can you help me to learn more?
(Another definition for planer that I've seen is " Carpenter sometimes".)