I have created a page view taxonomy/term/%/faq. It works fine but I need to replace taxonomy/term/% with its url alias.
Pathauto just allows you to generate the URLs automatically so I believe you would still have the issue.
You will need something like https://www.drupal.org/project/path_alias_xt to extend the alias functionality to the other subpaths like the node/%/edit, taxonomy/term/%/faq etc.
Try using pathauto which will help you create aliases for taxonomy pages.
Then i copied default taxonomy_term view to a new one using different URL (different than /taxonomy/term/%), i added a block (and disabled 'page' displayID) to this view acting exactly like default taxonomy_term view page.
Note : this block should have a contextual filter that correspond to taxonomy term ID (with depth or not)
Then i added this created block in my panel.
That allows to do what you are needing (get alias for URLs), and moreover, you can add things (blocks) to this page and it is a lot more flexible than overriding default taxonomy_term view. I did not this for that puprose, but you can get your goal this way.