Correspond after a duke gets fit (8)
I believe the answer is:
adequate
'fit' is the definition.
(thesaurus)
'correspond after a duke' is the wordplay.
'correspond' becomes 'equate' ('equate' can be a synonym of 'correspond'**).
'after' means one lot of letters go next to another.
'duke' becomes 'd'.
'a'+'d'='ad'
'equate' put after 'ad' is 'ADEQUATE'.
'gets' is the link.
(Other definitions for adequate that I've seen before include "Sufficient or all right" , "Enough to meet a purpose" , "Satisfactory, good enough" , "'Satisfactory, acceptable (8)'" , "up to the job?" .)