This sphere of activity isn't quite the real one (5)
I believe the answer is:
realm
'this sphere of activity' is the definition.
'realm' can be an answer for 'sphere' (synonyms). I'm not sure about the remainder of the definition.
'isn't quite the real one' is the wordplay.
'isn't quite' means to remove the last letter (not quite all of the word).
'one' becomes 'me' (a setter might use 'one' to humourously mean 'me').
'real'+'me'='realme'
'realme' with its final letter taken away is 'REALM'.
Can you help me to learn more?
(Other definitions for realm that I've seen before include "Monarchy" , "the UK, perhaps" , "Dominion" , "Kingdom could be lamer" , "Area of influence" .)