I added a new custom view to my Outlook Tasks but it automatically put it at the end of the Current View list in the Outlook Tasks Home Ribbon:
Obviously I want it in the top row so I don’t have to go digging. You can’t drag and drop them in either the “Manage Views…” dialog box or in the UI. I found this on a quick search: https://answers.microsoft.com/en-us/outlook_com/forum/all/outlook-contacts-can-you-arrange-the-views-in-the/8e6d9609-a57f-47e2-af3c-74fa54bb8faf
TL;DR – you can’t manually rearrange them…
But that doesn’t make sense because I clearly have in the past. “Maybe it only shows four ‘custom’ views or it’s (somehow) alphabetical,” I wondered. To test this, I went to “Manage Views…” I copied a View and renamed it and… it automatically sorted all of my custom Views in alphabetical order to the top of the list!
It seems that any rename will trigger this re-sort.