What is the legally permissible method for a financial transaction in which the annual rent is paid to the landlord in a single installment at a reduced price, and then the rent is collected from the tenant in two installments at the original price, whether this is in a new lease contract or the renewal of an old contract, taking into consideration the proposed conditions or necessary amendments for this?

The first method mentioned in the question is impermissible because it is akin to selling a debt for less than its value, which falls under usury (riba). Similarly, in a rental contract, it is not permissible for the tenant to stipulate to the owner that if the property is not rented to another party, the contract becomes void; this is an invalid condition. As for the Shariah-compliant method, it is for one to rent the property with an option clause (khiyar al-shart (definition)) for a known period. If a new tenant arrives, a new rental contract is made with them, and the first contract proceeds. If no one new comes, the first contract can be rescinded due to the presence of the option clause, provided that the Hanbalis' condition is met, which stipulates that the rental period should not commence immediately after the contract.