The only Emirate that has a rental law is Dubai.
Pet Ownership is not mentioned in the same law as a reason to evict a tenant. Landlords which do not have a clause in their contract that is particularly prohibiting pet ownership, have no legal base to ask a tenant to move out. Furthermore, Tower Managements cannot restrict pet ownership in their buildings. To do so, the building needs to have one single standard contract for all tenants to make sure, that the prohibited pet ownership can be taken care of. If a Person is the owner of its own apartment, and the sales contract is not prohibiting the pet ownership, such a prohibition cannot implemented just like this later on. Demanding fine payments because of pet ownership is illegal as well. No security company or tower management has the right to ask for fines, this would be only possible if all sales agreements contained a clause referring to such fines in the house rules of the tower.
Harassing pet owners or demand them to not use facilities (e.g elevators) as like other tenants is illegal and punishable by law. While pet ownership is not illegal in the UAE, harassing a person because of his pet is illegal. Harassment is considered a crime.
As for all other Emirates we do strongly recommend to always have a the written approval for the pet ownership from the Landlord. Again security companies or tower managements have no legal rights to harass tenants for their pet ownership, especially if the landlord approved the same, but in case a complaint is arising and the Municipality is visiting a tenant, the supportive letter of the Landlord is clarifying the legality of the animal in the premise.