Joining the New Camp is a very long-winded process in Gothic Remake. Alongside handing out a bunch of swampweed for cash, you also need to help the Rice Lord. And after completing the A Few Drops Too Much quest, this so-called lord of rice will set you the task of finding Bran in the Up to His Neck quest.
Take note that while this quest will earn you the trust of the Rice Lord, a major step in joining the New Camp, you'll make that decision with Lares later. In other words, it won't lock you out of joining the other camp factions. Before you start this quest, I also recommend grabbing some armour, especially the free Digger's Dress.
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