NorrCompetition uses the standard Joomla notifications handler. If you do not get any notifications from NorrCompetition then you should check:
Open Control Panel > Components > NorrCompetition > Options > General tab. Find Notifications on Entries parameter and make sure that it is not empty.
Make sure that in Global Configuration Send Mail parameter is enabled:
Control Panel > Global Configuration > Server > Mail Settings. If it is enabled and still nothing then try to change the Mailer:
Make sure that server is sending mails. On some hosts mail function can be incorrectly set. You can explore the logs or request the support from hosting provider.