It sounds like the iPhone 13 Pro will use next-generation LTPO displays which will feature ProMotion, too.

LTPO stands for low-temperature polycrystalline oxide and it will enable the iPhone to have a variable refresh rate. LTPO displays were previously rumoured to be only coming to one device, but analyst Ross Young from Display Supply Chain Consultants says the new displays will be available on both Pro models

The iPhone 12 Pro displays were rumoured to use ProMotion variable rate technology, which automatically adjusts the display to cope with the type of content being displayed, so for fast-moving video the refresh rate would automatically spin up.

The tech is already on use on iPad Pro, but reportedly didn't come to the iPhone as yet due to the impact on battery life. However, it's thought this wouldn't be so much of an issue with an LTPO display. 

The refresh rate would be able to rise to 120Hz for improved fluidity and responsiveness. Interestingly, it could also mean that Apple Pencil will be supported on iPhone - the iPad Pro with ProMotion offers a 20ms latency. 

The new LTPO displays are rumoured to be manufactured by long-term display partner Samsung.