I rented a movie from iTunes store and downloaded it on my Mac. It does not appear on my iPad. iCloud is on.

Rented movies can only be on a single device at a time.

A Movie rented on a Computer will not appear on an iOs device unless it is physically transferred to it. Once its transferred to the iOS device, it will disappear from the computer.

A Movie rented on an iOS device or Apple Tv can only be watched on the iOs device or Apple Tv that rented it, and cannot be transferred to another device.

About renting movies from the iTunes Store - Apple Support

I did this. On the MacBook in iTunes, it shows the movie is on my iPad, but when I go to iPad, I can't find it anywhere. I looked in iTunes and in the Video app, but can't find it. I've done this before and it worked, so I have no idea why I can't find it now, unless Apple has found a new cleverer interface to hide it in?

If it was successfully moved to the iPad, it should be in the Videos app. In a tab titled Rentals.

If you are not getting a "Rentals" menu option in the iPad Videos App, make sure the transfer wad complete from iTunes, and reset the iPad by holding down the home and power/sleep buttons together for 10 or 15 seconds or until the Apple Logo appears on screen. Let the iPad Reboot.