Recognised criminal in digs due this (13)
I believe the answer is:
distinguished
'recognised' is the definition.
('distinguish' can be a synonym of 'recognize')
'criminal in digs due this' is the wordplay.
'criminal' indicates an anagram.
'in'+'digs'+'due'+'this'='indigsduethis'
'indigsduethis' with letters rearranged gives 'DISTINGUISHED'.
(Other definitions for distinguished that I've seen before include "Treated as different" , "Noble and dignified in appearance" , "saw the difference" , "Uniquely recognised" , "Recognised - famous" .)