I'm currently writing a story about a psychopathic serial killer that meets a detective (the murderer owns a restaurant and the detective and his wife meet him there) that is investigating the victims of his. One thing that has me inching is that I don't know how to raise the stakes for the characters. While the characters are mostly great, with the villain with his own engaging aspects (his charisma, taste, master manipulator etc.) and the detective with his sympathetic side, I feel like I don't know how to set the stakes for my killer to focus on his next victims (he kills people that either annoyed him in some way or got in his way) and what the detective knows. So I would like any recommendation on how to make their relationship more dynamic.
How much research have you done into serial killers? Because serial killers tend to be classified in one of two broad categories: Organized and Disorganized. The former will plan his crimes out over time, observe his target, make notes about the environment, take steps to hide or destroy evidence, and target people in a population with a lot of transience. They can go for long stretches of time without killing, which compounds the problem. Disorganized killers tend to kill irrationally and leave a lot of evidence of their attack. In both cases, the reason they killer kills is more compulsion to kill... they get some kind of emotional high from their murder.
The two also get caught in different ways, with organized killers tending to end up trying to outsmart cops pursuing them, or thinking they can, and getting too arrogant. Disorganized killers tend to be brought down pretty quickly comparatively quickly as there tends to be more evidence and odd behaviors associated with the killer, though they tend to have difficulty tying the scenes together because disorganized killers tend to use weapons in their environment than a signature weapon.
One technique that police almost always use when they suspect a serial killer is operating in the area is withholding information from the press that would link the killer to the crime by knowledge. Suppose your killer always leaves a Yellow Rose at his scene as a calling card, the police might tell the press and public that the killer left a rose... which the public would first think is a Red Rose... if a person mentions Yellow Rose to the cops, it's likely they know something about the crime (details are omitted from just singular murders too, just in case patterns emerge. Also the placement of the flower might be left unsaid... usually the detail is so unusual, that it's almost telltale of the killer's work and can give away copycats as well).
One thing to note is that organized killers can, over time, devolve into disorganized killers which is how they get caught (Both Ted Bundy and Jeffery Dahmer were very organized at first, and ended up getting caught after becoming disorganized in their methods.).
My advice is to make sure that your characters have some flaws that could be used by the end of the story. The murderer could have some part of his sentence that was spoked wrongly or his change of attitude that sets off the detective instincts in the detective.
Hope this helps!