There are several different quest to obtain some special jobs in Final Fantasy XI, usually when your character level reach 30 there will be a quest to obtain some different advance job. But as you may know this advance job isn't more powerful and overpowered than the basic jobs, they only have some special skill that will help other party member in hunt or leveling. Here was some list of Advance job quest in Final fantasy XI.
PALADIN
Last back and talk to Balasiel, then talk to the guards on 2nd floor at the guard post east and west Cahaurme(J-9) & Baurise(H-9). Then go to Davoi (E10) and examine the discussed well and get an item. Go back to Balasiel and you will get a Lv 28 Kite Shield, and now you can change your job to a Lv. 1 Paladin.
DARK KNIGHT
Talk to Gumbah (Bastok Mines J-7)get the quest. Then go to the 3rd floor of Palbrough Mines (G-8). Get on the ship back to town and after the ride in the Zerhaun mines you'll recieve a 2 handed sword called the Chaos Bringer(?). Equip the sword and kill 100 of any type of enemies without leaving the area. After the 100 or more kills goto the person named Beadeaux located at the Southeast exit of the Pashhow Marshland and you get Dark knight. Now start working on your lv 1 Dark Knight. Dark Knight is, in my opinion, the coolest
job ever.
BEAST MASTER
RANGER
BARD
SAMURAI
Trade the old iron to the point at the far west of Konschtat Highlands (D8). A bomb enemy, Forger, will appear. Kill it and you will receive the iron fillings. Even if you fight this bomb with a party, it will only drop 1 item, and you can only trade iron every 3 minutes.
Use an axe at the mark point on the huge tree at the west side of The Sanctuary of Zi'Tah. A Walking Tree enemy, Guardian Treant, will appear. Kill it and examine the mark again to receive the branch.
Return to Jaucribaix with these items. After you give him them, he will tell you to come back in three days (3 hours). Come back and you will receive the Samurai job class and an Unsigned Sword. You can now change to Samurai in your Mog House.
DRAGOON
Now head to the Maze of Shakrami to excavate at the "Excavation Point" (G-7),(I-6), etc., not "Fossil Rock", for a "Dragon Egg". Go back to Cathedral and speak with Morjean. You should then accept the quest given by Yachemidot. Go to the Meriphataud Mountains. To the east at (K-8) will be the end of the Drogaroga's Spine. There will be a npc there.
Trade the egg to the npc and an event will occur. Go back to Sandoria and enter Chateau d'Oraguille. Then enter into Royal Knights' Quarters(H-9) and speak to Rahal and receive a key item. After receiving the key item, go to Ghelsba Outpost. Locate the "Hide Door"(G-10) in the Ghelsba Outpost and defeat the Dragon. The daron is behind the dorr, and only one party can fight it at a time. Bring a good party(6 people)of lv 45s to take it down.
NINJA
Get ready and click on it to fight 3 Korroloca Leech (Leech type NM), You may want to clear the area of Thread Leech's since they will start attacking you if they see you are fighting the Korroloca Leechs. After the fight click on the mark to recieve a key item. Now head back to Ensetsu in Port Bastok (I-5) and head to the new area Norg and speak to Ryoma to complete the quest.
SUMMONER
Now goto the House of the Hero in Windurst Walls. Investigate the door with the stone in your item list. After that, experience the 7 different weather conditions. You only have to have the weather effect on your map. You have to experience areas that are Pleasant, have Fire, Ice, Earth, Water, Wind, and Lightning, but not all at once.
After you have experienced those elements, head to La Theine Plateau. There is a stone circle there. Target and trade the stone into it. You will now obtain the Summoner job and your first summon which should be obvious after the quest.
Source(s) : IGN faqs