Back Her Majesty to be more authoritarian (7)
I believe the answer is:
sterner
'be more authoritarian' is the definition.
(authoritarian can mean strict)
'back her majesty' is the wordplay.
'back' becomes 'stern' (stern is a kind of back).
'her majesty' becomes 'er' (Elizabeth Regina).
'stern'+'er'='STERNER'
'to' acts as a link.
(Other definitions for sterner that I've seen before include "more inflexible anyway" , "More grimly serious" , "Renters of more strict sort" , "More demanding" , "More severe" .)