Officer extremely lucky as a rule (9)
I believe the answer is:
generally
'as a rule' is the definition.
(I've seen this before)
'officer extremely lucky' is the wordplay.
'officer' becomes 'general' (general officer is a kind of officer).
'extremely' means to remove the middle letters (only the extremes of the word are used).
'lucky' with its centre removed is 'ly'.
'general'+'ly'='GENERALLY'
(Other definitions for generally that I've seen before include "most of the time" , "Usually, as a rule" , "In most cases, as a general rule" , "For the most part" , "In most cases, usually" .)