How to notify an agent if a note is added to a ticket by a third party?

If a note is added by a third party (reply to a ticket forward), as of now Freshservice would not have a default email notification which would be sent to the Agent. Instead, you would have to configure a Workflow Automator(Admin-->Workflow Automator) to send out the Email Notifications in such cases.

Trigger: 

1. When these actions are performed by Requester 

2.  When these events occurred: Note added is Private

Condition:

1. On tickets with these properties: Leave Blank

Action:

Set status as Open

1. Set Status as 'Open' or any custom status (optional)

2. Send email to Assigned Agent

3. Type in your Content of the email