Apple's podcast directory
For many years, Apple Podcasts has been the largest and popular podcast directory on the Internet.
Podcasts Connect is a portal for podcasters like you, where you can add new podcasts and manage your existing ones.
To get your podcast published on Apple Podcasts, you need an Podcasts Connect (or Apple) account. You can open one here: https://appleid.apple.com/account#!&page=create
In addition, do not forget that your podcast must be published with at least one episode before submitting it to iTunes.
The initial waiting time is 2-3 days. After the initial wait, new releases in your podcast will be displayed on Apple Podcasts without much delay.