You can customize your Round Settings > Confirmation Page to add custom code that sends data elsewhere after a user finalizes their submission.
You just need to click the Source button to link to or add your code. You'll probably want to send data from the submission like the application ID and other specific information - you can do that using the Insert Variable link (the variables will be replaced by submission data):
You can even hide those variables using CSS in the Source view if you don't want applicants to be bothered with all the additional information.
Keep in mind when inserting code into the Confirmation Page there is no guarantee it will run before the applicant navigates away.
You might also consider using our REST 275and JS177 APIs to send data using code that's hosted elsewhere or directly from the submission form. Overall this would be a more advanced approach that would take additional effort to implement over adding a bit of code to the Confirmation Page but you'll have many more options and functionality available going this route.
OpenWater developers are also available at an additional cost to build and maintain more robust integrations.