My ideal Beastmaster would be a Tank rather than a DPS, functioning as effectively the opposite of the Arcanist: your character strides up to take the beating, throwing out enmity combos and keeping all of the enemy's attention on themselves, while the pet handles damage dealing. Most of your focus would be on commanding and positioning the pet, rather than just sort of having them around to do stuff occasionally.

One of the primary mechanics would have to be Catch, the old Beastmaster standby. Have it work like Mercy Stroke: a strong attack that can only be used when the target's HP is low. But rather than restoring some HP to the user, it captures the enemy for later; then, the Catch command becomes the Release command, where you unleash the stored creature on unsuspecting foes. Most of them would simply be a more powerful basic attack, but you could get interesting with some effects (such as, say, the Morbol family). And naturally, their Artifact gear would be the sheep suit.