Add new smarty template to an existing page
I am assuming you want to add some stuff at the bottom of the activity page, correct?

First of all, you need to establish if you are adding to a civicrm page or form. You can do a little test with the hook buildForm (see https://docs.civicrm.org/dev/en/latest/hooks/hook_civicrm_buildForm/) and check the formName or with the hook pageRun (see https://docs.civicrm.org/dev/en/latest/hooks/hook_civicrm_pageRun/) and check the name of the page.

Once you have established which hook you need to use you can add the template with the CRM_Core_Region.