When you encounter or realized that above no add new button issue on your WordPress site, it means you are not able to add theme or plugin the normal way.
Always when you try to access plugins or theme pages you will get an error below.
Kindly follow below steps in order to fix it.
Please note that this is for a none multisite WordPress installation.
Steps to fix it No Add New button
Access your site files using FTP, or File manager
Locate wp-confg.php file in the root directory
Open it with an editor and look for below line of code
define('DISALLOW_FILE_MODS', true);
Change the above code to below
define('DISALLOW_FILE_MODS', false);