Hey there @Ellen17268 - great question! I have not been asked this before, nor did I immediately know the answer. So I tested out some things for you and now I can help! Thank you for posting this topic. 

It turns out that on an iPad, you cannot “long-press” (with your finger) an event type in order to drag and drop it, allowing you to rearrange your event types. I know - this is what we’d all assume would be possible on most devices with a touch screen - what a bummer! That said - it’s possible with a bluetooth mouse! If you do not already have one, you can pick up a bluetooth mouse at most dollar stores for just a few bucks, as well as at stores like Five° Below and even Walgreens!

• Once you’ve got a bluetooth mouse, read the instructions for putting it in “pairing mode” for that first-time connection
• Connect your bluetooth mouse to your iPad via bluetooth
• Log into Calendly in the web browser you use (I did this in Google)
• You’ll then be able to click on any event type, drag and drop it wherever you’d like, effectively rearranging event types just like you can on a desktop/computer of any kind
• Once you’ve done this, check out your live booking page - your event types should now be in the desired order that you set them up to display in

I just used my bluetooth mouse after connecting to my own iPad to click, drag, rearrange and drop event types in my Calendly account - so yes, it’s possible! 

I hope this helps!