There are a few vocations you can get before the post games ther are:

gladiator-get someone to use dragon slash (sword) during high tension(100)

armamentilists-use wizard ward (mage) then make the person who used wizard ward to do final blow

ranger-use toxic dagger abillity (thief) and beat 3 chimra hobus with only poison

paladin-use whipping boy (warrior) 10 times to save party members not include the person whos using it (does not need to have low health)

There's also the Sage & Luminary Vocation.
The Sage vocation if I remember correct is killing 5 Boss Troll with Frizz ( I think it was Boss troll at least )
And the Luminary vocation is post game only where you have to kill 2(?) Moai Ministers with Hotlick.

Gladiator can be unlocked in Alltrades Abbey lower floor.
Armamentilists can be unlocked on the upper floor of Alltrades Abbey.
Ranger can be unlocked in the map after the Cabin leading to Zere Rocks.
Paladin can be unlocked at the rooftop of Gleeba.
Sage can be unlocked inside the Gittish Palace by reading a book.

To elaborate on yaybongo's answer:

In order to unlock the Armamentalist vocation, you must erect a Wizard Ward while fighting a Metal Slime specifically, and have whoever cast Wizard Ward make the killing blow before the Metal Slime runs away.

In order to unlock the Gladiator vocation, you must get a party member to a state of super-high tension while fighting a Slime, and then have the character in super-high tension use Dragon Slash to kill the Slime.

Not sure yet on the specifics of Ranger and Paladin, but so far, all of the quests I've found that unlock new vocations have very specific requirements regarding the monsters you need to defeat and how to defeat them.