Fear is common and a perfectly normal, innate, and adaptive behavior in all animals. However, if fear isn’t addressed, it can develop into serious behavioral and health problems. If your cat is showing fear or shyness, deal with it proactively. Many cats are fearful at first in a new environment and need a little time to adjust. They slowly become more confident as they get used to their living space and daily routine. Going to a new, strange environment can cause a fearful cat to regress at first in a new home.
The amount of time it takes a cat to settle into a new home varies from case to case. Some cats may take a week; others may take months, depending on their individual personalities. At first you should confine your cat to a small, quiet room. Provide appropriate hiding spots for them but make sure they can’t hide in any inaccessible places (e.g. closet or under the bed). These hiding places should be easily accessible and comfortable. Place the litter box within easy reach of the cat, but away from food and water. Keep your cat confined until they feel comfortable in the room and shows signs of wanting to explore the surroundings. Let your cat explore the rest of the house gradually (too much territory all at once may be overwhelming). If at any point during this process your cat regresses, confine them back to their “safe” room for a few days and start over by only allowing access to one room at a time. It’s best to ignore your cat and let them investigate on their own terms. Talk softly and move slowly around the cat. Encourage play with interactive toys (e.g. cat dancer or fishing pole type toy). Some cats are very play-motivated and regular play sessions can help bring them out of their shell and out of hiding. Try not to startle your cat.
If the behavior is not improving or worsens, consult with a professional