The Commander of the aerial forces of the HMT is Lasan Skyhorn and we see him and his eagles aid the Horde back in Bfa.
For the Zandalari that job falls to Raal
But no one ever talks about the initial mountes units of the Horde. The Wyverns. Just like the Wildhammer Clan for dwarfs they form up a core theme of the new Horde. So why did Blizzar fail to create a cool lore character who can take over this job?
Make it make sense.
If I recall correctly, the horde’s last aerial force used to be the Dragonmaw Clan with their Protodrakes. 
I’d argue that its pretty hard to give wyverns a spotlight because the horde aerial forces are straight up more diverse than the alliance.
As Breakercog said the dragonmaw are one such example but you also have troll and forsaken batriders, zandalari pterrodax riders, zeppelins and other goblin auxiliaries.
Wyverns are less a capable force and more symbolic warbeasts of status like human braided stallions.
We stopped having dragons as mounts so it makes sense to push wyverns like the alliance does with Gryphons.
Yeah I always considered Wyverns to be the Hordes counterpart to gryphons, but they’re not really showed off that much unfortunately.
Srsly I have seen batriders more by now then I did Wyverns sadly.
The only rider whose name I can summon is Mulverick, though even that’s a silly movie reference so I barely count it.
The reality is that the Wyverns (Which later became “Wind Riders” before going back to being Wyverns for… some reason…) just aren’t a part of any Orc group’s actual culture. They’re just some random animals that they happened to stumble upon when wandering around Stonetalon during WCIII.
iirc Cairne actually points them out to Thrall.
Cairne Bloodhoof: Hmm. The Oracle’s wisdom belongs to all. Perhaps the wyrvens that live nearby can be use to us? They have no love for hostile intruders!
They’re ugly, everyone knows they’re ugly, and their idle mid flight looks dumb.
It seems they are not very popular.