Although moving doesn't involve introducing a new pet to the household, it does involve introducing all your existing pets to a new home, with new smells and outdoor spaces.
Make sure you plan ahead of time what will happen to your pets on moving day. Unfortunately, the combination of strange happenings and people around the house, and the presence of open doors and windows, makes house-moving a particularly high risk period for dogs and cats straying from houses, even if this is completely out of character for them.
Many people chose to put their dogs and cats in kennels or catteries for a couple of days around the house move, which keeps them away from the stress and disruption of the process, safe and secure. If you're planning to do this, make sure your pet's vaccinations (including kennel cough vaccination for dogs) are up to date ahead of time, and make sure you have a firm reservation for their stay as soon as possible.
If kennelling isn't practical, then it's important to make sure they are kept secure during packing and loading of house contents. Ideally confine them to a quiet room with the windows and door locked (or a big sign on the door reminding everyone not to open it) with their food, water, bedding, and litter tray as required. Ensure you have a secure pet carrier for cats, as it is potentially very dangerous - for them and for you - for them to travel loose in the car. It is not appropriate for pets to travel in a removal van, as accidents and unforeseen delays may occur. Do not be tempted to open carriers if you stop for rest breaks on your drive, unless all car doors are completely closed, as frightened cats do sometimes escape and run away under these circumstances.
On your arrival, try to make a secure, comfortable den in a quiet room in the new house, as you did before your departure, and again keep doors and windows securely fastened while there are lots of 'comings and goings'. Straying from a new house is particularly hazardous as your pet will not know where they are, and may not be able to find their way back again if they are scared and run off.
Cats should be kept indoors for at least two weeks or longer. If you have moved a small distance of a street or two, they may try to return to their previous home. It can be very useful to let old neighbours and the new occupants of your old home know about your cats, and to ask them not to encourage them by feeding or allowing them in the house if they are seen in the area.