The Teldrassil Hippogryph is an Alliance-only mount that is obtainable during the Battle for Azeroth pre-patch. You an only get this mount during this War of the Thorns pre-event, and if you're too late for that, then there is no way you will ever be able to get it. Edit: It is now too late to get it!
So, to get the Smoldering Reins of the Teldrassil Hippogryph you will need to finish the pre-patch quest line. This quest line will begin automatically when you log in to a level 110 character, and the first step is to talk to Anduin in Stormwind. The next quest will send you to Astranaar and eventually Darkshore. Keep doing this quest chain, and by the end of it you will get the Smoldering Reins of the Teldrassil Hippogryph that will unlock the Teldrassil Hippogrpyh for all your Alliance characters.
The pre-event is divided into three separate parts, and a new part opens each week. If you read this at the end of July, then you will still need to wait another week before the third and final part unlocks.