Notification when the status on sql server replication is "Not Running"
Could you please let me know if there is a way we can receive alerts when the status changes on a particular replication.


You can achieve that using Replication Alerts

e.g. Below will set up alert for Replication: agent retry. Note that you must have database mail enabled and configured as well as sql agent operator configured.

EXEC msdb.dbo.sp_add_alert @name=N'Replication: agent retry', 
        @message_id=14152, 
        @severity=0, 
        @enabled=0, 
        @delay_between_responses=0, 
        @include_event_description_in=5, 
        @category_name=N'Replication', 
        @job_id=N'00000000-0000-0000-0000-000000000000'


Refer to : All About Automatically Monitoring Replication Agent Failures