Agent entering capital, backing monarch (7)
I believe the answer is:
emperor
'monarch' is the definition.
(emperor is a kind of monarch)
'agent entering capital backing' is the wordplay.
'agent' becomes 'rep' (short for representative).
'entering' means one lot of letters goes inside another.
'capital' becomes 'rome' (capital of Italy).
'backing' shows that the letters should be reversed in order.
'rep' put inside 'rome' is 'rorepme'.
'rorepme' back-to-front is 'EMPEROR'.
(Other definitions for emperor that I've seen before include "chap such as Charlemagne" , "Supreme ruler" , "Character in 24 ac" , "Japanese version of the king" , "Sovereign and richly-colored butterfly" .)