While Blizzard has been very dismissive of any question about the future of Dragonflight beyond Season 3, there might be something in the data indicating an upcoming Season 4.
They've done it before with Patch 9.2 when they added both Season 3 and Season 4 Vicious Saddle mounts in a PTR build. Originally neither mount had a source listed, but later on, we found out that the Croaker was the Season 3 reward and the Wolf the Season 4 reward.
This time around, they seem to have done it with the Gladiator mount.
The Dragonflight Season 3 Gladiator Mount is the Verdant Gladiator's Slitherdrake, which we datamined earlier this week. However, there is a second Gladiator mount that was added with Patch 10.2 PTR, Violet Gladiator's Drake.
The mount doesn't have an item, so likely means the name is not final.
With this, it seems that Blizzard is planning for a Season 4 in Dragonflight and, following the Dragonflight «theme», it will be based around the Blue Dragonflight. Much like Season 3 with Season 2's mount, the Season 4 mount is a recolor of the Season 1 mount, Crimson Gladiator's Drake, instead of using a new Dragonriding mount as the base.
If true, this will leave only the Bronze Dragonflight without a Season themed after them. I guess Dragonflight ran out of time for it.