It may be better for you to suggest to the Agent/ Landlord that you on to a "rolling contract" at the current rent ("Lesser Rent") until the renovations are complete and then, with a backstop date, by which the renovations must be completed. In exchange, you will be happy to sign/ enter a new Tenancy Agreement, with the higher Rent, when the works are complete.
In the alternative, theoretically, you could specify in the New Tenancy Agreement that you pay the Lesser Rent until the renovations are done by, and specify such a date by which they must be completed, further if the backstop date is missed, then you continue to pay the Lesser Rent but are also free to leave the Tenancy with say, 1 month Notice (Break Clause).
Please do not sign a Tenancy Agreement that you are not happy with!
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