increasing rent for tenants on housing benefit

Housing Benefit Overpayment

Can I get away with using Section13 notice to increase rent for tenants on housing benefit without issuing new tenancy agreement?

In the past I have found it easier to issue a new ast so that even the dimmest council official can understand what the level of rent is. I am facing a scenario where I do not really want to issue a new ast but do want to increase rent to the new / higher level of LHA which has gone up since the old ast was issued some 2 years ago.

Reasons why I don't want to issue a new AST include 1. having a validly served s21 notice which would no longer be valid and 2. There is a guarantee in place which would be harder to enforce on a subsequent tenancy agreement.