Right to support the monarch (6)
I believe the answer is:
proper
'right' is the definition.
(I know that right can be written as proper)
'support the monarch' is the wordplay.
'support' becomes 'prop' (prop up can mean to support).
'the monarch' becomes 'ER' (abbreviation for Elizabeth Regina, British Queen).
'prop'+'er'='PROPER'
'to' is the link.
(Other definitions for proper that I've seen before include "Actual" , "Right or suitable" , "name someone's given" , "Conforming to etiquette" , "Refined" .)