Getting the quest to build your ship!
You need to be lv 52, have finished Irdich and arrived to Irdich/Rebels Refuge. After you finished the quest "Charles Confession" you will get a quest called "Treasure on the Dump" from Charles de Doucer.
Next quest is "Here, give it to me" that sends you to Buzzing Family in the south.
Next quest is "Treasures of Astral Depths":
Fight Mechanoids to collect 10 high-powered batteries and install them on the small boat. Fly through
several anomalies and use the Experimental Stabilizer to destroy them, then return to the Buzzing
Family.
• High-powered Battery 10/10
• Barge equipped
• Sail set
• Stabilizer tested in an anomaly 5/5
(You need to activate the stabilizer before flying through the anomaly.)
Now last quest in Irdich is "Building an Astral Ship", this will send you to the Astral Academy to Maurice de Ardeur for League or Yaver Yevgini for Empire
Now you have to wait 10 days till your ship is build
If you enter the Astral Hangar, you can have a look at your unfinished ship by talking with Glowy Family (League) or Nomarkh Hanotep (Empire)
Once the 10 days passed, go into the hangar and you will get a popup to give your ship a name. Now you can summon your ship.