Unfortunately, you won’t be able to ride the Direhorses straight away.
Instead you’ll be left to your own devices to explore the forest biomes.
When do you get a Direhorse in Avatar: Frontiers Of Pandora?

You’ll need to reach the14th main mission ‘The Wandering Clan’so you can unlock Direhorse traversal.
Specifically, this is when you travel to the Upper Plains section of Pandora and meet the Zeswa Clan.
This means you’ll first have to complete the Aranahe main missions.
The bond, unlike that with your Ikran, will be temporary.
You won’t have to worry about leaving your Direhorse behind anywhere.
Instead, you could simply make a bond with another one in its stead.
You must approach your Direhorse of choice slowly and go for the ‘Soothe’ prompt when it appears on-screen.
When you are close enough, you’ll receive the option to make the connection.
This will cement the Direhorse into your service.
Although, it may be just as easy to establish a new bond.
As your bond is fresh, it will need to trust you more before answering your call.
Specifically, by completing ‘The Wandering Clan’ and ‘Hunters Hunted’ main quests.