How to auto-run a php script when certain condition is true?

Question

for example something like

if(new_user_registered() == true):
   send_success_mail();
endif;

I want to execute the script independent from user-end since too much stuff happening on user registration is slowing down the forum submitting process resulting in inappropriate and missing data.

Due to client privacy cannot reveal too much about the project. And I am a relatively new in programming so my explanation might not be that clear sorry for that in advance.