Operating system with staff keeping one engaged (7)
I believe the answer is:
android
'operating system' is the definition.
(Android is an operating system for mobile phones)
'with staff keeping one engaged' is the wordplay.
'with' becomes 'and'.
'staff keeping' becomes 'rod' (I am not sure about this - if you are sure you should believe this answer much more).
'one' becomes 'i' (Roman numeral).
'engaged' means one lot of letters goes inside another (inserted letters are taken in or engaged).
'rod' placed around 'i' is 'roid'.
'and'+'roid'='ANDROID'
(Other definitions for android that I've seen before include "Automaton resembling a human" , "Human-looking robot" , "Robot resembling 17" , "Robot resembling human being" , "Human-seeming robot" .)