I needed to add a newly created MySQL user with no access to any database with no special permissions (user is created from phpmyadmin) with some permissions to a specific database which is used for the operation of a website, here are the MySQL CLI client commands I issued to make it work:
# mysql -u root -p
mysql> GRANT ALL ON Sql_User_DB.* TO Sql_User@localhost;
mysql> FLUSH PRIVILEGES;
Where in the Example Sql_User_DB is my example database to which the user is granted access and my sample user is Sql_User .
Note that without FLUSH PRIVILEGES; new privileges might not be active.
To test further if all is fine login with Sql_User and try to list database tables.
$ mysql -u Sql_User -p
mysql> USE Sql_User_DB;
mysql> SHOW TABLES;