No, if a tenant does not agree to the new terms and refuses to sign the addendum, they cannot be legally held to it. The only option in that scenario is to wait until the lease is up for renewal and then introduce the new provision. If the tenant wishes to continue the tenancy, they will then need to agree to the new terms and sign the lease. So while it’s a bit of a gray area when the tenant doesn’t agree, it highlights the importance of including as many relevant terms as possible when initiating a new lease agreement.
Additional Comment: Indeed, this is why changing terms mid-lease can be challenging. The best approach is to ensure that the initial lease agreement is as comprehensive as possible. While you can introduce updates to a lease with an addendum later, you need mutual agreement, and trying to make changes without that can create friction between the landlord and tenant.