1. Create TeacherFactory.pm:

   package TeacherFactory;
   use Teacher;
   use strict;
   
   sub create_teacher {
       my ($class, @args) = @_;
       return Teacher->new(@args);
   }
   1;
   [download]

2. Make a list of all files that call Teacher->new.
3. Insert near their tops a use Teacher; statement.
4. Search and replace teacher constructions with factory requests.

That's the easy part; you have a pretty boring factory. Now make it interesting :)

Most likely, you may find that some calls to Teacher->new give you insufficient information to make the decision about whether a Lecturer or a teacher is required. Refactor your code *after* you have the above in place to either defer or advance the construction, depending on what makes more sense. But move in small steps that don't leave your code unstable.