Feathermanes are a tameable family of winged 'hybrid' beasts, introduced in Patch 7.2. Members of the family include gryphons, hippogryphs, owlcats, wolfhawks and wind riders (also known as 'wyverns').
As a Hunter, how can I tame Feathermanes?
Feathermanes aren't instantly tameable - you have to earn the privilege! Here's what you need to achieve first:
The Power Ascended pre-requisite was removed in Battle for Azeroth, as artifacts can no longer be levelled.
Since Battle for Azeroth, you can purchase this as any spec - not just Beast Mastery.
You must have completed the Order campaign for Hunters, leading to the achievement A Glorious Campaign, and then the Legionfall quest campaign, leading to the achievement Breaching the Tomb. The Legionfall campaign will not progress very far until you've completed the Order campaign.