I think this should be the class that turns players into completionists of collectables, so it's time to give some feedback while it's still early in development. I will be using alot of in game systems that are in place today with little tweeks to try to make the design realistic
The Beastmaster core( Beast, Pets -minion, Mounts, DOH Job Access)
When a beastmaster is out in the open world it has access to passive DOH skills like (One with the Forest, Truth of the Mountains) when using a node it could switch gear sets to a DOH class, use DOH class skills, then switch back to Beastmaster as if you were using a Transformation Macro.
The Beastmaster comes with a dismount attack from the mount which leads to how the chocobo fights with you on Gyashl Greens.
I know not all creatures, minions, and mounts share the aesthetic of a beastmaster and if that’s a problem then place a flag for beatmaster usable on them.
Beast(The Player Slots)
Beast design should be based on the chocobo mount and breeding/races system in game which consist of levels, class tree (healer, tank , dps) but can be unique based on family, abilities at breakpoints on the class tree, stats based on food ate like chocobo races, and barding/equipment with easy to understand stats or effects. Each beast having visible equipment is a lot of work, so if you start with the barding system being invisible, then if it becomes popular and worth the development you could make the barding visible.
Minions-pets(Summoner Summonings)
Similar to the Summoners elements system(Fire, Earth, Wind) the beastmasters system can be replaced with (healer, tank, dps)(side: note this could be beast family instead). You can slot a number of minions to summon like a carbuncle going to use 3 for this example. When you summon a minion they perform a skill, have a on summon effect that affects other Beast(The Player Slots), and can override beastmaster skills like Summoner's Gemshine ability to (range, gap closers, shields, and, weapon skill combos). To give an example of play and rotation: Say you run 3 minions from the wasp family that have the roles of dps, dps, tank. You would Summon the minions and it would do their spell and party effects like playing Summoner with the Gemshine ability. This would build a gauge, and once the gauge is full you can activate a weapon skill combo. The weapon skill combo based on your summoning order is a burst window; it could be like poison dart, winged dash, to poison armor in this example. Giving your rotation a nice fresh feel based on how you summon your minions to build gauge. The weapon skill hotkey can work like pvp so it doesn't have to be hard to execute on the player.