You can export candidates from a list directly to your ATS.
From whatever list you're in, select a candidate on the left-hand side. You can select more than one candidate if you'd like, and still perform the same actions listed below:
Once you have selected a candidate (or multiple candidates), you'll notice a grey option bar appear at the top of the list:
From there, you can choose which ATS you would like to export that candidate to. If you have not yet set up an integration with your ATS, you can do so by following the instructions here.
The candidate(s) that you selected are now exported to your ATS! When you log in to your ATS, you can view these exports under the appropriate candidates tab.