Firstly, a landlord will be concerned that your pet could damage or accelerate wear in their property, so make sure you take all reasonable steps to assure this won't occur.
That way, when you next move, you can ask your landlord/property manager for a good reference and this will place your next rental application streets ahead of competitors.
Secondly, it's important you accept that animals do increase wear on carpets. Fur and odours can build up, despite the best vacuum cleaners, so a quality carpet clean, at your expense, is the minimum expectation of your landlord.
Finally, dogs and cats can annoy neighbours with barking or unwelcome over-fence visits. Ask your neighbour for a reference to prove your pets are well managed.
Do these 3 things and you'll lessen any risk of doubts about your next application, making it far easier to succeed. In fact, tenants with pets often stay longer and that’s always in the interests of the landlord.
PET REFERENCES ARE THE WAY TO GO WHEN MOVING