Apple Podcasts is by far the largest directory of podcasts and submitting yours from Simplecast is fairly straight forward.
Start by making sure you fill out as many fields as you can for your podcast. Adding an accurate description, keywords, category, and a high-quality image are all very important. You can read more about Apple's requirements on Podcasts Connect FAQ.
Visit this link to go directly to the Apple Podcasts submission page. It will take you to a Podcast Connect login page, where you'll be asked to sign into your Apple ID if you are not already.
On the podcast submission page, copy and paste your Podcast RSS Feed URL (example— https://rss.simplecast.com/podcasts/[yourpodcastid]/rss) into the form and click submit. Once submitted, you may have to wait up to 48 hours for you podcast to be reviewed. You should be notified via email when your podcast is accepted. Read more about submitting to Apple Podcasts on Apple's site.
★ Apple does an excellent job of keeping their Podcast Connect articles and tutorials up to date. Connect's entire knowledgebase can be found right here.