A tenant gave notice to terminate her tenancy on the proper form N9, she has now changed her mind and decided to stay. Can I enter into a new agreement with her and charge her a new rent?

If the tenant gave notice to terminate her tenancy but then decides to stay, you have the option of applying to the Landlord and Tenant Board to enforce the notice to have her move out, or allow her to stay. However, if you allow her to stay you would not be able to enter into a new agreement, the original tenancy agreement would continue under the same terms.