I tenant leaving, the other remaining

I have 2 tenants in one property in their 7th month of a 6 month AST. 1 of which has given me a months notice to leave, the other wishes to stay. As the remaining tenant cannot afford the rent on her own, I need advice on how I can proceed, as a new tenancy agreement will need to be signed once the other tenant leaves.
I am prepared to reduce the rent slightly for 2 months, to give the existing tenant time to either find another flat mate, and also giving her 2 months notice at the same time in case she can’t find anyone.
Is this legal? i.e. can I get her to sign a 2 month rental agreement, and give her 2 months notice at the same time?