update tbl_NMR_users set `tbl_NMR_users_FirstName` = CONCAT(`tbl_NMR_users_FirstName`,' TESTING') Where `tbl_NMR_users_RegNumber` = '156330';

Notice the space in the appended portion, otherwise you just tack right on with no separation.
If your original value is null you can use this:
CONCAT(IFNULL(email_data, ''),' $email_data')
This will add it on to a null value as the first value in the entry

Append Data to Field in MySql

MySQL