Do I have to upgrade to edit a site built on 1.3 version of cakephp

Cake 1.3 now is more than 5 years old. If you want to do some small changes, just go ahead, it will work - except if you are using PHP 7.

For bigger changes the best way would be rewrite the whole thing for CakePHP 3.

I would not reccomend to update it. Resons are here: Upgrading from 1.2