Re-ordering fields in the Contact list
Navigate to the contacts section and click on the list settings button at the top-right corner of the interface:
Then, once you're on the list settings page, you'll be able to drag and drop fields into whatever order you want via the dotted icons shown below.
Finally, click save on the bottom or top of the page to keep any changes you've made. These changes will impact both the order of the fields on the Contact list (for the entire team), and also for all the individual contact pages.
Note: These features are only available to team admins.