Mounts in World of Warcraft: Legion Patch 7.1
It's always possible there are hidden mounts that nobody has found yet, but these are all the ones we're aware of.
Index
Mounts added to the 7.1 database, but not released (coming in 7.1.5, 7.2 or later) :
Coursers
With the new PvP season comes a new Prestige reward mount. This one is achieved at rank 8. (The original was rank 4).
Falcosaurs
These four feathered and beaked raptors are associated with a series of falcosaur invasion world quests around the Broken Isles. Two are available in Patch 7.1 and two will only be attainable once The Nighthold raid is open, which is slated for "mid to late January". They're awarded at the end of a long chain offered by their equivalent companion pets. For more information on capturing the companion pets and starting the quest chains, see the detailed blog post by Quintessence of WarcraftPets.
Skeletal Steeds
A colour variant of the fancy new skeletal steed model drops from the new version of Attumen the Huntsman in the Return to Karazhan dungeon in Patch 7.1. There are four other colours that have existed since Beta but are so far unavailable, except as temporary mounts.
The following are unassigned looks, not yet used for mounts :
Skates / Sting Rays
One colour of this new aquatic mount is available from Galissa Sundew, the fishing vendor on Darkmoon Island. There are three other colours that may appear in the future.
The following are unassigned looks, not yet used for mounts :
Hawkstriders
This hawkstrider uses the original model from the Burning Crusade, but in a colour that has never been available until now. It's a reputation reward for the new Talon's Vengeance faction which requires you to first obtain a Falcosaur mount (see above!), then speak to Aviana in Highmountain, and finally gain reputation through a PvP grind.
Wolves
This wolf is the Horde reward for the Legion PvP world quest meta-achievement, Free For All, More For Me. This involves completing each of four different PvP-related world quests 20 times each.
Horses
This horse is the Alliance reward for the Legion PvP world quest meta-achievement, Free For All, More For Me. This involves completing each of four different PvP-related world quests 20 times each.
Mounts added to the Patch 7.1 database but not coming until later
Basilisks (Patch 7.1.5)
The new basilisk mount model will be available in the revamped Brawler's Guild, which is scheduled to open in Patch 7.1.5. While green is the only colour currently assigned to this model, any of the non-mount basilisk skins could be used, resulting in four other potential colours for the future.
The following are unassigned looks, not yet used for mounts :
Manasabers (Patch 7.1.5?)
This fancy new Manasaber is a brand new colour and sports different armour to the original. It's apparently a reward for completing the quest, 'The Fate of the Nightborne' in Suramar, but we currently have no information about the quest. It's quite possible that it'll require The Nighthold raid to be open, which is slated for "mid to late January".
A bunch of PvP-related mounts first appeared in the Legion Beta database but were later removed. Many have reappeared in the Patch 7.1 database but not the in-game journal. We aren't sure if this is deliberate or a mistake. We'll update this section as we find out more.
Coursers (uncertain)
There are six colours of unicorn-like Coursers. Two were introduced as Prestige Honor (PvP) mounts at Legion launch. The following four have appeared in the database for 7.1 but they probably won't appear until later PvP seasons.
Stormdrakes (uncertain)
Four colours of armoured Stormdrake were assigned at launch to be the Gladiator's Arena Season rewards for Legion. The remaining two colours (below) were removed again but have returned to the database in 7.1. The format of their names suggests that they are also Arena Season mounts but that would indicate six seasons, which would be unusual. Perhaps they'll come from other PvP-related sources.
Stormcrows (unused)
A new arcane-purple colour of Stormcrow mount has appeared in the 7.1 database. It doesn't seem to have been assigned to an official mount and may be intended for other purposes, or delayed until a later patch.
Firecats (mystery mounts!)
A "Fire Cat Mount" model has appeared in the 7.1 database, but its files are locked so we don't yet know what it looks like. For what special purpose has it been created? Your guess is as good as ours!