Landlords could be required to tell potential new tenants how much rent they charged previous tenants in a property. This transparency would make things fairer for tenants. It could encourage landlords not to raise rents much when tenants change in the same property. The transparency requirement could also cover the previous 3-5 years rent. If landlords want higher rent, they would need to explain why: for example, making substantial upgrades to the property between tenancies.
However, this wouldn’t actually limit rent increases. In the current market where housing supply does not meet demand, a new tenant might still need to pay much higher rent than the previous tenant – just to get a home.