On this page of our guide to Greedfall we have provided a detailed walkthrough to Contraband side quest.
Where to start the quest?: New Serene, conversation with Manfred.
Go to a tavern and question the innkeeper in New Serene - ask him about his problems with merchandise. Now go to the docks and question the Customs Officer. Talk to him and you will find out about the missing key. You'll find it at the end of the pier, pick it up and open a nearby chest. Tell the customs officer about the evidence found in the chest. Bribe him or use your intuition.
Now go to the indicated spot and hide behind a wooden fence. After a cutscene, you will have a choice - you can save Alric, or start chasing "Egon". It is worth to jump down and help Alric, because "Egon" can be caught later. Talk to the rescued man and you will get a job to find the dispensary.
Travel to Hikmet. Then go to the indicated place and you will come across some guards. Tell them that you want to enter no matter what, and they'll throw themselves at you - kill your opponents. A little bit further you'll encounter more enemies, including Captain Ludwig. Defeat your enemies and then speak to Ludwig.
Go back to New Serene and talk to governor Manfred. You will complete the quest and get get 1600 XP. Also, you will receive 3 reputation points with Coin Guard. In addition, you will immediately start the Dirty Traffic side quest.