@EliseP Welcome to the community, it’s lovely to have you here and I will gladly help you.
I am just looking at my app for reference to assist further and I am sorry that you are unable to see new sits first.
I am not sure what device you are using as I have an iPhone, but when I search for a location on the app all of the sits that appear first in the list are marked as new and this is the same when I view my saved search list any that are new (within the last 24 hours) are at the top of the list and then I can scroll down to view the older ones.
I do have one saved search in a location that does not have many sits, so none are marked as new as they have been posted for a few days and the new badge has dropped off.
Also if you are seeing the same listing as new again, it might be when the owner declines all of their previous applicants the listing gets posted again. Owners with certain membership levels also have the option to boost their listing making it new again.
If you are continually not seeing new listings at the top of your app search or saved search then it might be best for the Membership Services Team to look into your account as they can also view your account in an app view and check that everything is working okay.
You can reach out to them at support@trustedhousesitters.com and sending screenshot examples can also help.
Also feel free to ask any more questions (you can also start a new topic) about how to get started as there are lots of experienced members here that will be happy to help you get on your way with your sitting adventure 
If you add your sitters profile to your listing other members can view it and give you feedback.
Here is how to add it:
If you need any help just let me know.