After rescuing Greirat from his cell in the High Wall of Lothric, he will return to Firelink Shrine and offer his services as a merchant. To advance his questline, you'll need to send him out on a scavenging mission. His first destination is the Undead Settlement.
Before sending Greirat to the Undead Settlement, ensure you have defeated the Curse-Rotted Greatwood boss. This is a crucial prerequisite, as Greirat will not offer to scavenge until this boss is down. Once the Greatwood is defeated, speak with Greirat at Firelink Shrine. He will ask if he can go scavenging for you. Agree to his request.
Greirat will then depart from Firelink Shrine. You can continue with your own exploration and progression. He will return after you have defeated any boss in the game, or after a significant amount of time has passed and you have reloaded the Firelink Shrine area multiple times. Upon his return, he will have expanded his inventory with new items, including:
- Firebombs
- Throwing Knives
- Kukri
- Exploding Bolts
- Large Leather Shield
- Knight's Crossbow
- Long Bow
- Standard Arrow
- Large Arrow
- Wood Arrow
- Standard Bolt
- Heavy Bolt
- Wood Bolt
This initial scavenging trip is relatively safe for Greirat, so you don't need to worry about any specific actions to ensure his survival at this stage. Just send him off and continue your journey.