"We call the police for them to look for this person."
Translation:On appelle la police pour qu'ils recherchent cette personne.
Afin que is "in order that" or "so that." Often pour que and afin que can be used interchangeably and both trigger the subjunctive mood, but the register is much more formal with "afin que", just like "in order that" is in English. Here I believe either will work, but I will verify with our French grammarian.