Archbishop, strait-laced, dined (7)
I believe the answer is:
primate
'archbishop' is the definition.
(thesaurus)
'strait-laced dined' is the wordplay.
'strait-laced' becomes 'prim' ('prim' can be a synonym of 'strait-laced').
'dined' becomes 'ate'.
'prim'+'ate'='PRIMATE'
(Other definitions for primate that I've seen before include "Metropolitan" , "Archbishop, for instance" , "Highest order of mammal" , "bishop, perhaps" , "Man in the mitre" .)