Predatory cats represent your ability to go out on the prowl and bring what you want into your life. They can also refer to your ability to protect your best interests. If the predatory cat is after you in a dream then this part of you is trying to get your attention because it wants you to acknowledge it and use it in your life. Do you need to take on the role of a hunting beast right now? If the cat is friendly then this part of you is working well for you.
For a woman, any sort of cat in a dream can often symbolize her sexuality, her inner sex kitten. Again, if the cat is after you then this part of you needs attention!
A cheetah in particular can sometimes refer to someone who is a “cheater” in real life.
Cheetahs are also known for their great speed and may be a nudge from your subconscious to hurry up and finish something.