The Rent Control Law of 1983 applies to the rental of property in what are known as 'Controlled Areas' – and the property must have been completed by 31st December 1999. Rent rises for Cypriots and other EU citizens in these properties is limited. I believe that currently rent increases are controlled at 0% and this will remain unchanged until 21st April 2019.
For properties not covered by the Rent Control law and/or non-EU citizens it's an open market. Rents are negotiated; increases are driven by market forces and are not controlled.