Removing a rat is beneath Her Maj (7)
I believe the answer is:
erasing
'removing' is the definition.
(to erase something is to remove it)
'a rat is beneath her maj' is the wordplay.
'rat' becomes 'sing' (both can mean to inform on someone).
'is beneath' says to put letters next to each other (in a down clue).
'her maj' becomes 'ER' (Elizabeth Regina ie Her Majesty Queen Elizabeth).
'a'+'sing'='asing'
'asing' after 'er' is 'ERASING'.
(Other definitions for erasing that I've seen before include "obliterating memory" , "Getting rid of" , "Removing" , "Rubbing out" .)