The Painter is locked in the upper floor of the library at the end of the Corvian Settlement. Guarded by Sir Vilhelm, he must be defeated to obtain the key that unlocks the staircase to her location. After freeing her from the library, she'll move to the attic in Ariandel Chapel.
The Painter's role is to paint a new world which will replace the current rotting Painted World. For that she needs flame and a pigment from the Dark Soul of man. However, her job was delayed by her imprisonment in the Corvian Settlement by Friede and Ariandel, suppressing the flame with his own blood. Therefore, after freeing her from the library, the Ashen One's goal would be to unlock the passage to Father Ariandel and defeat both him and Sister Friede in battle, after which the Painter could start painting her new world in the chapel's attic. After defeating Gael in The Ringed City, the Ashen One may give her the Blood of the Dark Soul for her to paint.
"I believe... I feel the scent of ash upon thee. Thou'rt the one whom Uncle Gael spoke. The one to show me flame. Tis good. When this is done, may I return. The door is open thanks to thee. Tis good, I'll head off to paint. I promised Uncle Gael I would."
After relocating to the Cathedral
"Thou'rt Ash. Thou'st a pact made with Uncle Gael. So I wish to tell thee all. Behold its size. This is my canvas. It's to be a cold, dark and very gentle place. ...But first, I must see flame. I wish to paint a picture. Of a cold, dark and very gentle place. One day, it will make someone a goodly home. That's why I must see flame."
After defeating Sister Friede
"Those who aren't ken to fire cannot paint a world. Those absorbed by fire, must not paint a world. Don't worry, I haven't forgotten, Mother... I can hear the fire crackle..."
Talking to her after killing her
"Ashen One, I cannot die, I have a world to paint."
After finding The Ringed City
"...Ashen One, thy gift of flame has taken root. And Uncle Gael will soon bring the pigment. Pigment coloured like the dark soul of man. I wonder if Uncle Gael has found it? The pigment coloured like the dark soul of man."
After giving her the pigment
"My thanks, Ashen One. With this will I paint a world. Please tell me thy name. I would name this painting after thee."
Tell her your name
"My thanks. I will paint a world of that name. Twill be a cold, dark, and very gentle place. And one day, it will make someone a goodly home."
I don't have a name
"I see. We are much alike. Then I will name this painting "Ash". Twill be a cold, dark, and very gentle place. And one day, it will make someone a goodly home."
Keep talking afterwards
"I wonder when Uncle Gael intends his return. I hope the new painting will be to him a gentle home. My thanks, Ashen One. I will assuredly finish the painting.Of a cold, dark, and very gentle place. One day, it will make someone a goodly home."