Gilbert can be found inside a house near the Central Yharnamlamp, where the Hunter can speak to him through a window, whereby he provides warnings of the dangers of the city, as well as some sense of direction.
He is critically ill, and journeyed to Yharnam in the hopes of finding a cure for his disease, alas, he knows that the scourge is affecting him and grows increasingly sick and desperate as times passes. He is one of the few outsiders in Bloodborne.
After killing Rom, and triggering the Blood Moon event, returning to Gilbert's house will reveal the window has been smashed open from the inside, and a Beast Patient (male) can be found wandering the area just outside. This Beast is heavily implied to be Gilbert, and can be killed for the weakest form of the ClawmarkCaryll Rune.
Click to see dialogue
Oh you must be a Hunter, and not one from around here either. I'm Gilbert, a fellow outsider. You must have had a fine time of it. Yharnam has a special way of treating guests. I don't think I can stand if I wanted to, but I'm willing to help, if there's anything that can be done. This town is cursed. Whatever your reasons might be you should plan a swift exit. Whatever can be gained from this place, it will do more harm than good.
Paleblood, you say? Hmm... Never heard of it. But if it's blood you're interested in, you should try the Healing Church. The church controls all knowledge on blood ministration, and all varieties of blood. Across the valley to the East of Yharnam lies the town of the Healing Church, known as the Cathedral Ward. And deep within the Cathedral Ward is the old grand cathedral. ...the birthplace of the Healing Church's special blood, or so they say. Yharnamites don't share much with outsiders. Normally, they wouldn't let you near this place, but... The hunt is on tonight. This might be your chance...
Yes, I see... But the great bridge is the only way to the Cathedral Ward. And during the hunt, the bridge is closed... Hmm... You could try the aqueduct? There's a rather, how shall I put it, colorful area south of the great bridge. From there, an aqueduct leads to the Cathedral Ward. Not a place you'd normally want to visit, but... I don't imagine you have much of a choice. Do you?
An aqueduct leads from the town, south of the main bridge to the Cathedral Ward. Not a place you'd normally choose to visit, but... Not much of a choice, with the bridge closed.*heavy coughing*
Ahh, you needn’t concern yourself with me. I’m afraid I’m of little help now. But before I… Take this…(he gives you the Flamesprayer) I made no use of it, but perhaps you… What inflicted me was incurable, but this town gave me hope… Their strange blood bought me time. I was most fortunate. Unharmed by the plague of beasts, I can even die human. *coughing*