Loop through database and run shell commands with Python and exiftool
Close your connection to your database, even if there's an error. Use a try-finally to do this.
Make some functions, moving the database stuff into it's own function makes it much easier to read.
From os.system docs:


  The subprocess module provides more powerful facilities for spawning new processes and retrieving their results; using that module is preferable to using this function. See the Replacing Older Functions with the subprocess Module section in the subprocess documentation for some helpful recipes.

You may want to use os.path for various file related things, such as os.path.join to join path sections.
print is slow. Try removing it for a massive speed up.


And so you may want to start changing your code to look like:

import mysql.connector
import os
import subprocess


def read_database():
    cnx = mysql.connector.connect(user='root', database='database', password='password')
    cursor = cnx.cursor()
    try:
        query = ("SELECT post_title,Event,File,Name from a order by File")
        cursor.execute(query)
        for item in cursor:
            yield item
    finally:
        cursor.close()
        cnx.close()


def main():
    path = os.path
    old_dir = r'/home/alan/Downloads/OLD/'
    new_dir = r'/home/alan/Downloads/NEW/'
    for (post_title, event, file_name, name) in read_database():
        old_file = path.join(old_dir, file_name)
        new_file = path.join(new_dir, post_title, file_name)
        if not path.exists(new_file):
            os.makedirs(new_file)
        if path.isfile(old_file):
            subprocess.call(["exiftool", "-q", old_file, "-xmp:title='" + post_title.replace("'", "") + "'"])
            subprocess.call(["exiftool", "-q", old_file, "-xmp:description='" + name.replace("'", "") + " courtesy of https://www.festivalflyer.com'"])
            subprocess.call(["exiftool", "-q", old_file, "-description='" + name.replace("'", "") + " courtesy of https://www.festivalflyer.com'"])
            os.rename(old_file, new_file)

if __name__ == '__main__':
    main()