I just finished reading Skin Game and on pg 242 Harry mentioned his first apprentice, Kim Delaney. I don't however remember her being mentioned prior but I blew through the series so likely just didn't file it away. So my question is when and where does he talk about her previously?
Kim Delaney is from Fool Moon. It's subtle and brief, but he does refer to her as an apprentice.
My stomach made an unhappy noise. It was almost as empty as my wallet. I would never have been able to afford dinner tonight, except that Kim had offered to buy, if I'd talk to her about something during the meal. A steak dinner was less than my usual rate, but she was pleasant company, and a sometime apprentice of mine. I knew she didn't have much money, and I had even less.
Fool Moon, Chapter One
Since the reference is so brief, presumably it wasn't as rigorous or impactful an apprenticeship as Molly's. A later passage implies it was just to help her get started, and he'd done as much for others before, but lessons went further for someone he liked.
Kim was one of several people I had coached through the difficult period surrounding the discovery of their innate magical talents. It made me feel like crap to withhold information from her, but she had been playing with fire. I couldn't let her do that. It was my respondibility to help protect her from such things, until she knew enough to realize how dangerous they were.
The fact that this brief attempt to protect her by keeping her in ignorance backfires horribly, and impacts the rest of the book, is probably a large reason why he takes his later apprenticeship of Molly much more seriously.
In Fool Moon, she approaches Harry Dresden at McAnally's, asking him to help her with a greater summoning circle, claiming it is for academic purposes. He refuses to give her the information, because he doesn't think that Kim has enough knowledge or experience to be messing with it, and knows that the White Council wouldn't want the dangerous information in the hands of a non-Council member. Angry at Harry for not telling her, Kim storms out of the bar.
When Dresden shows up at Harley MacFinn's house on Chicago's Gold Coast, he finds Kim dead. She was killed by Harley MacFinn when he transformed into the Loup-garou. She had been trying to recreate a circle that could hold in the werewolf, after his previous circle was ruined, but as she didn't know how to empower the circle properly, it had been unable to hold in the beast.