its very helpful to establish a good relationship with the cat before you begin pet sitting. For example, if you have the opportunity, spend time with the cat before you start pet sitting, such as by visiting them in their home or by playing with them. This will help the cat become more comfortable with you and reduce the stress of the transition.
Also when visiting the cat , also take note of the cat behavior and report to the owner any significant change if noticed, such as change in eating or sleeping habits, aggression or shyness, or even changes in vocalization.
It is also a good idea to be familiar with cat body language and behavior, this will help you to understand the cat better, and to identify any potential problems early on.
Finally, remember to enjoy the time with the cat and take lots of photos and videos to share with the owner!