When does hook_menu run? I need to edit the hook_menu function in my  module.  I need to add a new link to a menu, and edit the path for an existing link.  Is this possible without creating a whole new module?  

The only example in the docs for when hook_menu runs is when the module is enabled.  Is there any other time it runs?
Clearing the cache the menu and routing tables will be reconstructed.

In the admin UI, go to: 

/admin/config/development/performance

Using drush:

drush cache-clear all


Other methods are described here: How do I call the menu_rebuild function in Drupal 7?