Recognised immediately in outskirts of Kingston (5)
I believe the answer is:
known
'recognised' is the definition.
(thesaurus)
'immediately in outskirts of kingston' is the wordplay.
'immediately' becomes 'now' (I've seen this before).
'in' means one lot of letters goes inside another.
'outskirts of' suggests removing the centre.
'kingston' with its centre removed is 'kn'.
'now' put into 'kn' is 'KNOWN'.
(Other definitions for known that I've seen before include "Widely recognized" , "Acknowledged" , "Apprehended mentally" , "Famous" , "In the public domain?" .)