Image: Rebel Wolves / Bandai NamcoOfficial screenshot from Rebel Wolves / Bandai Namco.
Smuggler is earned by making 1,000 denarii from selling silver. The silver trader is only open to you during a window in the middle of the game, so it is easy to miss.
Once your Infamy is at least 4, find the silver trader in Svartrau and sell silver until your earnings from him reach 1,000 denarii.
Hoard silver as you explore and sell it in batches. Finish before your Infamy reaches 9, because after that you cannot get back into the city safely.