Do solitary? Her Majesty's pleasure for this one? (8)
I believe the answer is:
royalist
'her majesty's pleasure for this one?' is the definition.
(admirer or supporter of the monarchy)
'do solitary?' is the wordplay.
'do' indicates anagramming the letters (solvers must work out or 'do' the anagram puzzle).
'solitary' is an anagram of 'ROYALIST'.
(Other definitions for royalist that I've seen before include "Civil War Cavalier" , "opponent of Republicans" , "rightwinger?" , "Solitary (anag.)" , "One pro-monarchy" .)