The pet deposit is an increase in the security deposit in the lease and is made part of the security deposit for all purposes. Texas does not have any specific tenant pet laws.Landlords can create their own rules for pets and put them in your lease. Addendum to this Residential Lease Agreement. Here's a sample Pet Agreement for renters with guidelines for requirements, responsibilities and how to manage issues. It's essential for tenants to review and understand the pet policies outlined in the lease agreement before signing it. A pet addendum gives permission to allow the tenant to have pets on the rental property. It requires the tenant will be responsible for their pet(s). Pet clauses in lease agreements are provisions that allow tenants to have pets in their rental properties. This pet agreement is available for free download.