Just my ideas on how these two jobs can be added into the game. I loved the Time Mage in FF Tactics and Beast Master was always cool in FFXI, and I would love to see these two brought into the game.
We have already seen (Spoiler) use a type of magic that can be considered Time Magic. The "Break" spell used froze enemies in place. They also used gravity magic (levitate) which has always been part of Time Magic, so there already is president for it.
I can see Time Mage fitting in as either a DPS/Support caster. Many of their spells work as support for the party with only few damaging spells, so it can also be argued that they can be a Healer caster, healing wounds by reversing time to a point before being injured.

Now, Beast Master would be an tricky job to enter into the game. While precedent has already been set that this is a thing already in the games canon, implementing it would be interesting. Making it a Pet style job would be the obvious choice, but the devs have had trouble balancing that in the past, seeing as the Summoner job had changed so many times already that it 'Pet' isn't even a combatant anymore. But if they can find a way, I think making it a DPS Pet job would be the most logical way to go about it, just give the pet the similar AI as your Chocobo companion in battle...but different.
Another way to go about it is to make the Beast Master skills use the Pet as the attack.

Here's the Hot Take part of this post, I wouldn't want them to be unlocked only at high levels, such as Reaper and Sage.
I understand why many veteran players would want them unlocked near end game content levels, but I feel this hurts newer player experience and a stronger connection a player can have with the job. An personnel example I have would be Samurai. I have a friend who LOVES Samurai and would have loved to begin playing the game as one, but when I told him he would have to wait till level 50 and complete most of the ARR content, he noped out out right away. Some players just want to go through their MSQ journey as a specific job and not have to wait till way later in the game to do it.
But I wouldn't want the Veteran players to feel like they're being ignored again, so I have a compromise.

Similar to how Arcanist unlocked both Summoner and Scholar, keeping both of their levels together so when leveling one, the other also went up, I think the same thing should be done here with these two jobs. Time Mage could be used off of the Thaumaturge crystal. So any veteran Black Mages can quickly have a high level Time Mage right away, while newer players can go on their MSQ journey as one.
As for the Beast Master, being a job in FFXI that used a one handed weapon and shield, I can see this working off of the Gladiator job crystal. I always found it odd how a Gladiator would be become a holy knight with no other options. Beast Master seems like a good fit, just swap the sword for a 1-handed Ax.