I couldn't find Renew button in Apple Developer App on my iPhone too. The solution in my case was to go to the phone settings => Apple ID => Subscriptions. Select Apple Developer Program subscription in the list and click Renew. As Apple Support told me when I was initially subscribing I was logged in to my iPhone and to Apple Developer App with different accounts and now I need to renew subscription in iPhone settings under user #1 and not in Apple Developer App under user #2 who's actually bought the subscription.