Your problem is meta, solve it meta
Tell other players, including your DM, that you are planning to play this character that does justice serial-killing. Other characters might feel this character is shady, which is fine, but ask them not to uncover your hobby too quickly. Tell them that you want to develop this character, at least for x sessions.
The in-universe explanation would be that most people tend not to stick their nose in other's business, and respect each other doing in their time. Ask for your DM's cooperation.
- If they try to follow you, DM will say they lose you after a while (you should be trained in shaking pursuers, I guess?)
- If they become suspicious of you, ask the player to explain why their character became suspicious and what they are suspicious about. Everyone has secrets to hide, and they won't know exactly what you are doing
- Start stating where you will be hunting your prey after others state their whereabout. You can choose victims where other PCs are not there
- Basically, whatever they want to do, you always escape and no one knows/confronts you until the time to do so, which is when you say so
DnD is not a game of hide and seek, a competition where other players want to uncover your dark side, unless you are playing the villain. Even so, DnD is a game of story. What fun it would be if the villain is uncovered on first session and killed? Instead, ask their help to build the story, until the day where you think you want to play another character, when their suspicion is proven and this time you fail to escape and must accept the judgement.