Those beginning to scheme against reigning monarch (4)
I believe the answer is:
tsar
'monarch' is the definition.
(I know that tsar is a type of monarch)
'those beginning to scheme against reigning' is the wordplay.
'those beginning' indicates taking the first letters (the letters which begin the words).
The first letters of 'to scheme against reigning' is 'TSAR'.
(Other definitions for tsar that I've seen before include "Word derived from Caesar, used by European rulers since 1547" , "Once-powerful Russian" , "Rats to the Russian emperor" , "Despot" , "Autocrat" .)