Queen with fantastic cat, more than once her destroyer of rodents (3-7)
I believe the answer is:
rat-catcher
'destroyer of rodents' is the definition.
'queen with fantastic cat more than once her' is the wordplay.
'queen' becomes 'r' (r is abbreviation regina. e.g. in ER ).
'with fantastic cat' becomes 'atc' (I am not sure about this - if you are sure you should give a lot more credence to this answer).
'more than once' says to double the letters.
'atc' duplicated is 'atcatc'.
'r'+'atcatc'+'her'='RAT-CATCHER'
(Other definitions for rat-catcher that I've seen before include "Rodent operative" , "Vermin remover" , "Vermin exterminator" .)