The law treats animals as personal property so the first thing the executors will need to do is to check the will to see if any specific provision has been made for the pet. For example, there might be a legacy in favour of a friend on condition that he or she looks after the pet. If there is nothing in the will, then the animal forms part of the residuary estate, in other words, ownership of the animal will pass to those who have inherited the estate as a whole after money legacies and gifts of things have been dealt with. So the executors will need to discuss the pet problem with the beneficiaries. Usually a satisfactory practical solution can be worked out. Unfortunately, in some cases, the animal has to be put to sleep. Obviously it makes sense for any pet owner to think carefully about arrangements for the pet and make appropriate provisions in the will itself or in a letter of wishes which can be left for the guidance of the executors.
Animal charities do provide useful guidance and often encourage the pet owner to consider a donation in return for a charity taking responsibility for an otherwise homeless animal.