To rebook your Pet Sitter you need to go on their profile and send them a new booking request.
One way to reach their profile again is through the Contact Details tab you can find on any conversation with the sitter:
Another way is through the Favourite & recent sitters section of your profile:
If you should have any trouble with this process, you can always ask your sitter to initiate a booking with you, which you will only need to accept. Here's how.