You sure can. Meters are actually owned by the Networks and Metering companies, not the home owner, so you won't be breaking any terms in your lease by switching your meter! We do, however, encourage you to let your landlord or property manager know.
If you are in an apartment, installing a smart meter shouldn't have any impact on other apartment owners in the building, nor should it have an impact for any future tenants in the property.
If a new tenant decides to use a different retailer from Amber then they can keep the Smart Meter and use it with a new retailer at no cost from us.