Submitting your podcast to Spotify with Omny Studio is easy! 

Head to the playlist details section on the podcast that you'd like to submit and unfurl the 'submit to podcast directories' menu here:
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Select 'Submit to Spotify', then read the TCs and, if you're happy, agree to them by checking the checkbox:

Click 'Submit to Spotify' and you're done!

New podcasts may take up to 24 hours to appear in Spotify, however most podcasts appear within just a few hours.

Once your podcast is up, you can claim your Spotify Shows Portal stats by following this guide.