Number turning up in protest — who don't republicans want? (7)
I believe the answer is:
monarch
'who don't republicans want?' is the definition.
'number turning up in protest' is the wordplay.
'number' becomes 'no' (abbreviation for 'number').
'turning up' says the letters should be written backwards.
'in' indicates putting letters inside.
'protest' becomes 'march' (marching is a kind of protesting**).
'no' backwards is 'on'.
'on' placed inside 'march' is 'MONARCH'.
(Other definitions for monarch that I've seen before include "King or butterfly" , "Not a subject" , "Butterfly - ruler" , "one over realm?" , "Head of State" .)