Mature cats can be traumatized during a move to a new environment. All cats are very sensitive animals and any change in their environment can make them aggressive.
They prefer a quiet household and accept changes reluctantly. Cats are territorial by nature and need to feel secure in their environment in order to relax. They are naturally shy and should slowly be introduced to these new changes.
Stressed-out cats can be helped with environmental adjustments, such as limiting their territory to a single room for a while. Chances are, the cat will not eat or drink for a while until it becomes accustomed to its new environment. Place litter boxes in a quiet, private place that is easily accessible to the cat and where it will not be disturbed by children or ambushed by other pets.
Since this experience can be overwhelming for most cats, introductions to individuals, to strange surroundings, and to other pets should be very gradual. Existing pets should be gradually introduced to their new pal (stroke, praise and re-assure both equally) but they should not be left alone together until you are absolutely sure of their reliable behavior to each other.
It is important not to make too much of an issue of these 'meetings' or your existing pets will wonder what you are up to. Always stay with your pets for the first few meetings.
Extreme patience is required to help them adjust to their new environment. Creating a safe and stable living environment is essential.