Sub-letting

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Can I add a clause on the "Addendum Agreement" to allow sub-letting of rooms with-in my house, without invaliding the AST?

Background: I have a wonderful (mature student) tenant (and friend) that has happily lived in my property for 3 years, without any problems. We have had a verbal agreement until now, and she has let boyfriends and mates move in and out as she pleases. However the local council have noticed multiple residency and insist that I am therefore responsible for council tax, and must make back payments. So I'm writing an AST to prove/confirm she is the full tenant, and responsible for tax payments (of which she is exempt, as a student). However I wish to continue to allow her the ability to sub-let room to whom ever she wishes.