In general, most landlords will not allow tenants to have pets in their properties. However, there may be circumstances in which this can be considered, and you may want to allow it in some situations. As a landlord, your business will run much more smoothly if you have good tenants who remain in your property for many years. This might mean that you make some exceptions for particularly good tenants, like allowing them to have a pet if it will keep them in the property for longer.
It also depends on the type of pet and the ramifications for your property. For example, if a tenant wanted to have a small pet in a cage, this is unlikely to do any harm to your property. Something like a dog or a cat may be more detrimental. However, do bear in mind that if you have a disabled tenant, they may need to have an assistance dog.