Hiring/Renting: Setting the Rental Period to Begin at a Future Date
Practical Laws of Islam as per the teachings of Ayatullah Sistani
Ruling 2199
If a house is given on rent for a year, for example, and the beginning of the rental period is set to a month after the rental contract has concluded, the rental agreement is valid even if the house is being rented by someone else at the time of concluding the contract.
-Ayatullah Sistani, Practical Laws of Islam, Hiring/Renting (Ijarah)