I have found a way to do this.
Go to the app store app
click on your account (name with amount of $$ you have)
Click on 'Account Settings' on the top right (next to redeem gift card)
On the 'Account Settings' page, scroll down to 'Manage' section
Where it says 'Subscriptions' click 'Manage'
It'll take you through the renew dialog.
Apple, please fix your documentation, this is not okay.
Topic:
Developer Tools & Services
SubTopic:
Apple Developer Program
Tags: