Once you have decided to rent your property to a tenant with a pet you should include a pet clause in your tenancy agreement. An example of a pet clause would be:
“It is further agreed between the Landlord and Tenant that the Landlord grants permission for the Tenant to keep a pet {insert animal type and breed} named {insert animal name} (“The Pet”) in The Property for the duration of the Tenancy. The Tenant agrees not to keep or permit to be kept on the Property any further pets or animals of any description without the previous consent in writing of the Landlord.”
You may also wish to introduce a pet policy which sets out what is expected of tenants with pets while they are living in your property.