There is no RAW solution to get a dire hyena as a mount but here are some ideas that you can discuss with your GM.
1) Buy a dire hyena as a mount. The prize is up to the GM (should be ~300gp like a heavy combat horse because dire hyenas are common as mounts for gnolls) but with the 'Rich parents' trait you have 900gp available at 1rst level and that should be enough.
2) Take a class with an animal companion and use the 'wolf' animal companion stats for a hyena. Simply rename it. With the 7th level advancement it grows large and you can ride it.
3) Take the chevalier archtype 'Beast Rider'. At 4th level you can have very uncommon mounts like a snapping turtle (giant) or a tyrannosaurus. A dire hyena is not on the list but it should be ok with GM approval.
Additional mounts might be available with GM approval.
4) Play a summoner and design your eidolon like a hyena. At 8th level you can ride it.