I don't think so. I haven't come across any part where Annie is killed in those novels.
As far as I remember, Annie survives throughout the DCI Banks novels. There's no instance of her being killed. Maybe you got some wrong information or mixed it up with another character.
No, Annie isn't killed in the DCI Banks novels. The plot doesn't lead to such an event. Usually, these kinds of details are quite clear in the narrative and there's no indication of Annie's death.
Chapter 904, "Welcome Young Master and Young Madam!", is the clearest early answer because it turns Jiang Cheng's situation into a concrete plot event. The chapter turns that into something concrete by moving from Jiang Bufan and Jiang Buchen immediately ran up in surprise.
Chapter 853, "The Bracelet Worn by the Empress?!", is the clearest early answer because it turns Empress Zhaode's situation into a concrete plot event. The chapter turns that into something concrete by moving from Jiang Li carefully examined the branches and leaves for a while.
Chapter 766, "Young Master Gu, Please Come Inside!", is the clearest early answer because it turns Wen Jiaojiao's situation into a concrete plot event.
A practical answer is Chapter 13, because it turns the idea into a concrete scene. The chapter opens with Sensing that something was off with Jiang Yan, Jiang Yan dismissed the..., adds pressure through He probably had a good guess who it was., and ends on How could this happen..." Lin Manru.
Chapter 687, "How Did She Die Again?", is the clearest early answer because it turns Shao Changqing's situation into a concrete plot event. The chapter turns that into something concrete by moving from In the process of pursuing the Protagonist Group, she gradually came... to I'm busy here;
Chapter 600, "You merchants aren't even fit to carry my shoes!", is the clearest early answer because it turns Shen Ruobing's situation into a concrete plot event.
Chapter 777, "Backstage Buffs Stacked!", is the clearest early answer because it turns Jiang Shixu's situation into a concrete plot event. A useful checkpoint is the way the scene starts with Jiang Shixu also knew about his trending on social media.
Chapter 764, "Has Someone from the Rong Family Arrived?!", is the clearest early answer because it turns Lin Manru's situation into a concrete plot event. It opens with The banquet was nearing its end, and many guests had gradually left.
Chapter 856, "Hurry and Stop Work!", is the clearest early answer because it turns Jiang Li's situation into a concrete plot event. A useful checkpoint is the way the scene starts with Jiang Li looked towards the source of the commotion.
Chapter 776, "Sister Li Keeps a Toy Boy?", is the clearest early answer because it turns Weibo's situation into a concrete plot event. It opens with Apart from the two of them, some other users had started following...