Gilbert can be found at the window of the house right next to the Central Yharnam lamp.

If you return and speak to him after entering the Cathedral Ward he will hand over the Flamesprayer . You can return again after defeating Rom, the Vacuous Spider and Gilbert will have turned into a Beast Patient (Male) and can be defeated for his drops.

Drops:

• 222 Blood Echoes
• Clawmark Rune